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<title>GitHub - CAHLR/pyBKT: Python implementation of Bayesian Knowledge Tracing and extensions</title>
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<path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path>
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<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"executive_insights","context":"resources","tag":"link","label":"executive_insights_link_resources_navbar"}" href="https://github.com/solutions/executive-insights">
Executive Insights
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<button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false">
Open Source
<svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1">
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</button>
<div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4">
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<div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3">
<ul class="list-style-none f5" >
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<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"github_sponsors","context":"open_source","tag":"link","label":"github_sponsors_link_open_source_navbar"}" href="/sponsors">
<div>
<div class="color-fg-default h4">GitHub Sponsors</div>
Fund open source developers
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</a></li>
</ul>
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<ul class="list-style-none f5" >
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<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"the_readme_project","context":"open_source","tag":"link","label":"the_readme_project_link_open_source_navbar"}" href="https://github.com/readme">
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<div class="color-fg-default h4">The ReadME Project</div>
GitHub community articles
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</ul>
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<div class="border-bottom pb-3 pb-lg-0 border-bottom-0">
<span class="d-block h4 color-fg-default my-1" id="open-source-repositories-heading">Repositories</span>
<ul class="list-style-none f5" aria-labelledby="open-source-repositories-heading">
<li>
<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"topics","context":"open_source","tag":"link","label":"topics_link_open_source_navbar"}" href="https://github.com/topics">
Topics
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<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"trending","context":"open_source","tag":"link","label":"trending_link_open_source_navbar"}" href="https://github.com/trending">
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<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"collections","context":"open_source","tag":"link","label":"collections_link_open_source_navbar"}" href="https://github.com/collections">
Collections
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</div>
</div>
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<li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item">
<button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false">
Enterprise
<svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1">
<path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path>
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</button>
<div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4">
<div class="HeaderMenu-column">
<div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3">
<ul class="list-style-none f5" >
<li>
<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"enterprise_platform","context":"enterprise","tag":"link","label":"enterprise_platform_link_enterprise_navbar"}" href="/enterprise">
<svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-stack color-fg-subtle mr-3">
<path d="M11.063 1.456a1.749 1.749 0 0 1 1.874 0l8.383 5.316a1.751 1.751 0 0 1 0 2.956l-8.383 5.316a1.749 1.749 0 0 1-1.874 0L2.68 9.728a1.751 1.751 0 0 1 0-2.956Zm1.071 1.267a.25.25 0 0 0-.268 0L3.483 8.039a.25.25 0 0 0 0 .422l8.383 5.316a.25.25 0 0 0 .268 0l8.383-5.316a.25.25 0 0 0 0-.422Z"></path><path d="M1.867 12.324a.75.75 0 0 1 1.035-.232l8.964 5.685a.25.25 0 0 0 .268 0l8.964-5.685a.75.75 0 0 1 .804 1.267l-8.965 5.685a1.749 1.749 0 0 1-1.874 0l-8.965-5.685a.75.75 0 0 1-.231-1.035Z"></path><path d="M1.867 16.324a.75.75 0 0 1 1.035-.232l8.964 5.685a.25.25 0 0 0 .268 0l8.964-5.685a.75.75 0 0 1 .804 1.267l-8.965 5.685a1.749 1.749 0 0 1-1.874 0l-8.965-5.685a.75.75 0 0 1-.231-1.035Z"></path>
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<div>
<div class="color-fg-default h4">Enterprise platform</div>
AI-powered developer platform
</div>
</a></li>
</ul>
</div>
<div class="border-bottom pb-3 pb-lg-0 border-bottom-0">
<span class="d-block h4 color-fg-default my-1" id="enterprise-available-add-ons-heading">Available add-ons</span>
<ul class="list-style-none f5" aria-labelledby="enterprise-available-add-ons-heading">
<li>
<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"github_advanced_security","context":"enterprise","tag":"link","label":"github_advanced_security_link_enterprise_navbar"}" href="https://github.com/security/advanced-security">
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<path d="M16.53 9.78a.75.75 0 0 0-1.06-1.06L11 13.19l-1.97-1.97a.75.75 0 0 0-1.06 1.06l2.5 2.5a.75.75 0 0 0 1.06 0l5-5Z"></path><path d="m12.54.637 8.25 2.675A1.75 1.75 0 0 1 22 4.976V10c0 6.19-3.771 10.704-9.401 12.83a1.704 1.704 0 0 1-1.198 0C5.77 20.705 2 16.19 2 10V4.976c0-.758.489-1.43 1.21-1.664L11.46.637a1.748 1.748 0 0 1 1.08 0Zm-.617 1.426-8.25 2.676a.249.249 0 0 0-.173.237V10c0 5.46 3.28 9.483 8.43 11.426a.199.199 0 0 0 .14 0C17.22 19.483 20.5 15.461 20.5 10V4.976a.25.25 0 0 0-.173-.237l-8.25-2.676a.253.253 0 0 0-.154 0Z"></path>
</svg>
<div>
<div class="color-fg-default h4">GitHub Advanced Security</div>
Enterprise-grade security features
</div>
</a></li>
<li>
<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"copilot_for_business","context":"enterprise","tag":"link","label":"copilot_for_business_link_enterprise_navbar"}" href="/features/copilot/copilot-business">
<svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-copilot color-fg-subtle mr-3">
<path d="M23.922 16.992c-.861 1.495-5.859 5.023-11.922 5.023-6.063 0-11.061-3.528-11.922-5.023A.641.641 0 0 1 0 16.736v-2.869a.841.841 0 0 1 .053-.22c.372-.935 1.347-2.292 2.605-2.656.167-.429.414-1.055.644-1.517a10.195 10.195 0 0 1-.052-1.086c0-1.331.282-2.499 1.132-3.368.397-.406.89-.717 1.474-.952 1.399-1.136 3.392-2.093 6.122-2.093 2.731 0 4.767.957 6.166 2.093.584.235 1.077.546 1.474.952.85.869 1.132 2.037 1.132 3.368 0 .368-.014.733-.052 1.086.23.462.477 1.088.644 1.517 1.258.364 2.233 1.721 2.605 2.656a.832.832 0 0 1 .053.22v2.869a.641.641 0 0 1-.078.256ZM12.172 11h-.344a4.323 4.323 0 0 1-.355.508C10.703 12.455 9.555 13 7.965 13c-1.725 0-2.989-.359-3.782-1.259a2.005 2.005 0 0 1-.085-.104L4 11.741v6.585c1.435.779 4.514 2.179 8 2.179 3.486 0 6.565-1.4 8-2.179v-6.585l-.098-.104s-.033.045-.085.104c-.793.9-2.057 1.259-3.782 1.259-1.59 0-2.738-.545-3.508-1.492a4.323 4.323 0 0 1-.355-.508h-.016.016Zm.641-2.935c.136 1.057.403 1.913.878 2.497.442.544 1.134.938 2.344.938 1.573 0 2.292-.337 2.657-.751.384-.435.558-1.15.558-2.361 0-1.14-.243-1.847-.705-2.319-.477-.488-1.319-.862-2.824-1.025-1.487-.161-2.192.138-2.533.529-.269.307-.437.808-.438 1.578v.021c0 .265.021.562.063.893Zm-1.626 0c.042-.331.063-.628.063-.894v-.02c-.001-.77-.169-1.271-.438-1.578-.341-.391-1.046-.69-2.533-.529-1.505.163-2.347.537-2.824 1.025-.462.472-.705 1.179-.705 2.319 0 1.211.175 1.926.558 2.361.365.414 1.084.751 2.657.751 1.21 0 1.902-.394 2.344-.938.475-.584.742-1.44.878-2.497Z"></path><path d="M14.5 14.25a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Zm-5 0a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Z"></path>
</svg>
<div>
<div class="color-fg-default h4">Copilot for business</div>
Enterprise-grade AI features
</div>
</a></li>
<li>
<a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"premium_support","context":"enterprise","tag":"link","label":"premium_support_link_enterprise_navbar"}" href="/premium-support">
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<path d="M1.75 1h12.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 14.25 14H8.061l-2.574 2.573A1.458 1.458 0 0 1 3 15.543V14H1.75A1.75 1.75 0 0 1 0 12.25v-9.5C0 1.784.784 1 1.75 1ZM1.5 2.75v9.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h6.5a.25.25 0 0 0 .25-.25v-9.5a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Z"></path><path d="M22.5 8.75a.25.25 0 0 0-.25-.25h-3.5a.75.75 0 0 1 0-1.5h3.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 22.25 20H21v1.543a1.457 1.457 0 0 1-2.487 1.03L15.939 20H10.75A1.75 1.75 0 0 1 9 18.25v-1.465a.75.75 0 0 1 1.5 0v1.465c0 .138.112.25.25.25h5.5a.75.75 0 0 1 .53.22l2.72 2.72v-2.19a.75.75 0 0 1 .75-.75h2a.25.25 0 0 0 .25-.25v-9.5Z"></path>
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<div>
<div class="color-fg-default h4">Premium Support</div>
Enterprise-grade 24/7 support
</div>
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</ul>
</div>
</div>
</div>
</li>
<li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item">
<a class="HeaderMenu-link no-underline px-0 px-lg-2 py-3 py-lg-2 d-block d-lg-inline-block" data-analytics-event="{"location":"navbar","action":"pricing","context":"global","tag":"link","label":"pricing_link_global_navbar"}" href="https://github.com/pricing">Pricing</a>
</li>
</ul>
</nav>
<div class="d-flex flex-column flex-lg-row width-full flex-justify-end flex-lg-items-center text-center mt-3 mt-lg-0 text-lg-left ml-lg-3">
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<div
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<button
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<div class="mr-2 color-fg-muted">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-search">
<path d="M10.68 11.74a6 6 0 0 1-7.922-8.982 6 6 0 0 1 8.982 7.922l3.04 3.04a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215ZM11.5 7a4.499 4.499 0 1 0-8.997 0A4.499 4.499 0 0 0 11.5 7Z"></path>
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<span class="flex-1" data-target="qbsearch-input.inputButtonText">Search or jump to...</span>
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<div data-target="query-builder.styledInputContainer" class="QueryBuilder-StyledInputContainer">
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<span class="sr-only" id="query-builder-test-clear">Clear</span>
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click:query-builder#clear
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<template id="search-icon">
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<template id="code-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-code">
<path d="m11.28 3.22 4.25 4.25a.75.75 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.275-.326.749.749 0 0 1 .215-.734L13.94 8l-3.72-3.72a.749.749 0 0 1 .326-1.275.749.749 0 0 1 .734.215Zm-6.56 0a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042L2.06 8l3.72 3.72a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L.47 8.53a.75.75 0 0 1 0-1.06Z"></path>
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<template id="file-code-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-file-code">
<path d="M4 1.75C4 .784 4.784 0 5.75 0h5.586c.464 0 .909.184 1.237.513l2.914 2.914c.329.328.513.773.513 1.237v8.586A1.75 1.75 0 0 1 14.25 15h-9a.75.75 0 0 1 0-1.5h9a.25.25 0 0 0 .25-.25V6h-2.75A1.75 1.75 0 0 1 10 4.25V1.5H5.75a.25.25 0 0 0-.25.25v2.5a.75.75 0 0 1-1.5 0Zm1.72 4.97a.75.75 0 0 1 1.06 0l2 2a.75.75 0 0 1 0 1.06l-2 2a.749.749 0 0 1-1.275-.326.749.749 0 0 1 .215-.734l1.47-1.47-1.47-1.47a.75.75 0 0 1 0-1.06ZM3.28 7.78 1.81 9.25l1.47 1.47a.751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018l-2-2a.75.75 0 0 1 0-1.06l2-2a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042Zm8.22-6.218V4.25c0 .138.112.25.25.25h2.688l-.011-.013-2.914-2.914-.013-.011Z"></path>
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<template id="history-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-history">
<path d="m.427 1.927 1.215 1.215a8.002 8.002 0 1 1-1.6 5.685.75.75 0 1 1 1.493-.154 6.5 6.5 0 1 0 1.18-4.458l1.358 1.358A.25.25 0 0 1 3.896 6H.25A.25.25 0 0 1 0 5.75V2.104a.25.25 0 0 1 .427-.177ZM7.75 4a.75.75 0 0 1 .75.75v2.992l2.028.812a.75.75 0 0 1-.557 1.392l-2.5-1A.751.751 0 0 1 7 8.25v-3.5A.75.75 0 0 1 7.75 4Z"></path>
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</template>
<template id="repo-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-repo">
<path d="M2 2.5A2.5 2.5 0 0 1 4.5 0h8.75a.75.75 0 0 1 .75.75v12.5a.75.75 0 0 1-.75.75h-2.5a.75.75 0 0 1 0-1.5h1.75v-2h-8a1 1 0 0 0-.714 1.7.75.75 0 1 1-1.072 1.05A2.495 2.495 0 0 1 2 11.5Zm10.5-1h-8a1 1 0 0 0-1 1v6.708A2.486 2.486 0 0 1 4.5 9h8ZM5 12.25a.25.25 0 0 1 .25-.25h3.5a.25.25 0 0 1 .25.25v3.25a.25.25 0 0 1-.4.2l-1.45-1.087a.249.249 0 0 0-.3 0L5.4 15.7a.25.25 0 0 1-.4-.2Z"></path>
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</template>
<template id="bookmark-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-bookmark">
<path d="M3 2.75C3 1.784 3.784 1 4.75 1h6.5c.966 0 1.75.784 1.75 1.75v11.5a.75.75 0 0 1-1.227.579L8 11.722l-3.773 3.107A.751.751 0 0 1 3 14.25Zm1.75-.25a.25.25 0 0 0-.25.25v9.91l3.023-2.489a.75.75 0 0 1 .954 0l3.023 2.49V2.75a.25.25 0 0 0-.25-.25Z"></path>
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</template>
<template id="plus-circle-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-plus-circle">
<path d="M8 0a8 8 0 1 1 0 16A8 8 0 0 1 8 0ZM1.5 8a6.5 6.5 0 1 0 13 0 6.5 6.5 0 0 0-13 0Zm7.25-3.25v2.5h2.5a.75.75 0 0 1 0 1.5h-2.5v2.5a.75.75 0 0 1-1.5 0v-2.5h-2.5a.75.75 0 0 1 0-1.5h2.5v-2.5a.75.75 0 0 1 1.5 0Z"></path>
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<template id="circle-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
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</template>
<template id="trash-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-trash">
<path d="M11 1.75V3h2.25a.75.75 0 0 1 0 1.5H2.75a.75.75 0 0 1 0-1.5H5V1.75C5 .784 5.784 0 6.75 0h2.5C10.216 0 11 .784 11 1.75ZM4.496 6.675l.66 6.6a.25.25 0 0 0 .249.225h5.19a.25.25 0 0 0 .249-.225l.66-6.6a.75.75 0 0 1 1.492.149l-.66 6.6A1.748 1.748 0 0 1 10.595 15h-5.19a1.75 1.75 0 0 1-1.741-1.575l-.66-6.6a.75.75 0 1 1 1.492-.15ZM6.5 1.75V3h3V1.75a.25.25 0 0 0-.25-.25h-2.5a.25.25 0 0 0-.25.25Z"></path>
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</template>
<template id="team-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-people">
<path d="M2 5.5a3.5 3.5 0 1 1 5.898 2.549 5.508 5.508 0 0 1 3.034 4.084.75.75 0 1 1-1.482.235 4 4 0 0 0-7.9 0 .75.75 0 0 1-1.482-.236A5.507 5.507 0 0 1 3.102 8.05 3.493 3.493 0 0 1 2 5.5ZM11 4a3.001 3.001 0 0 1 2.22 5.018 5.01 5.01 0 0 1 2.56 3.012.749.749 0 0 1-.885.954.752.752 0 0 1-.549-.514 3.507 3.507 0 0 0-2.522-2.372.75.75 0 0 1-.574-.73v-.352a.75.75 0 0 1 .416-.672A1.5 1.5 0 0 0 11 5.5.75.75 0 0 1 11 4Zm-5.5-.5a2 2 0 1 0-.001 3.999A2 2 0 0 0 5.5 3.5Z"></path>
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</template>
<template id="project-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-project">
<path d="M1.75 0h12.5C15.216 0 16 .784 16 1.75v12.5A1.75 1.75 0 0 1 14.25 16H1.75A1.75 1.75 0 0 1 0 14.25V1.75C0 .784.784 0 1.75 0ZM1.5 1.75v12.5c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25V1.75a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25ZM11.75 3a.75.75 0 0 1 .75.75v7.5a.75.75 0 0 1-1.5 0v-7.5a.75.75 0 0 1 .75-.75Zm-8.25.75a.75.75 0 0 1 1.5 0v5.5a.75.75 0 0 1-1.5 0ZM8 3a.75.75 0 0 1 .75.75v3.5a.75.75 0 0 1-1.5 0v-3.5A.75.75 0 0 1 8 3Z"></path>
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</template>
<template id="pencil-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-pencil">
<path d="M11.013 1.427a1.75 1.75 0 0 1 2.474 0l1.086 1.086a1.75 1.75 0 0 1 0 2.474l-8.61 8.61c-.21.21-.47.364-.756.445l-3.251.93a.75.75 0 0 1-.927-.928l.929-3.25c.081-.286.235-.547.445-.758l8.61-8.61Zm.176 4.823L9.75 4.81l-6.286 6.287a.253.253 0 0 0-.064.108l-.558 1.953 1.953-.558a.253.253 0 0 0 .108-.064Zm1.238-3.763a.25.25 0 0 0-.354 0L10.811 3.75l1.439 1.44 1.263-1.263a.25.25 0 0 0 0-.354Z"></path>
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</template>
<template id="copilot-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copilot">
<path d="M7.998 15.035c-4.562 0-7.873-2.914-7.998-3.749V9.338c.085-.628.677-1.686 1.588-2.065.013-.07.024-.143.036-.218.029-.183.06-.384.126-.612-.201-.508-.254-1.084-.254-1.656 0-.87.128-1.769.693-2.484.579-.733 1.494-1.124 2.724-1.261 1.206-.134 2.262.034 2.944.765.05.053.096.108.139.165.044-.057.094-.112.143-.165.682-.731 1.738-.899 2.944-.765 1.23.137 2.145.528 2.724 1.261.566.715.693 1.614.693 2.484 0 .572-.053 1.148-.254 1.656.066.228.098.429.126.612.012.076.024.148.037.218.924.385 1.522 1.471 1.591 2.095v1.872c0 .766-3.351 3.795-8.002 3.795Zm0-1.485c2.28 0 4.584-1.11 5.002-1.433V7.862l-.023-.116c-.49.21-1.075.291-1.727.291-1.146 0-2.059-.327-2.71-.991A3.222 3.222 0 0 1 8 6.303a3.24 3.24 0 0 1-.544.743c-.65.664-1.563.991-2.71.991-.652 0-1.236-.081-1.727-.291l-.023.116v4.255c.419.323 2.722 1.433 5.002 1.433ZM6.762 2.83c-.193-.206-.637-.413-1.682-.297-1.019.113-1.479.404-1.713.7-.247.312-.369.789-.369 1.554 0 .793.129 1.171.308 1.371.162.181.519.379 1.442.379.853 0 1.339-.235 1.638-.54.315-.322.527-.827.617-1.553.117-.935-.037-1.395-.241-1.614Zm4.155-.297c-1.044-.116-1.488.091-1.681.297-.204.219-.359.679-.242 1.614.091.726.303 1.231.618 1.553.299.305.784.54 1.638.54.922 0 1.28-.198 1.442-.379.179-.2.308-.578.308-1.371 0-.765-.123-1.242-.37-1.554-.233-.296-.693-.587-1.713-.7Z"></path><path d="M6.25 9.037a.75.75 0 0 1 .75.75v1.501a.75.75 0 0 1-1.5 0V9.787a.75.75 0 0 1 .75-.75Zm4.25.75v1.501a.75.75 0 0 1-1.5 0V9.787a.75.75 0 0 1 1.5 0Z"></path>
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</template>
<template id="copilot-error-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copilot-error">
<path d="M16 11.24c0 .112-.072.274-.21.467L13 9.688V7.862l-.023-.116c-.49.21-1.075.291-1.727.291-.198 0-.388-.009-.571-.029L6.833 5.226a4.01 4.01 0 0 0 .17-.782c.117-.935-.037-1.395-.241-1.614-.193-.206-.637-.413-1.682-.297-.683.076-1.115.231-1.395.415l-1.257-.91c.579-.564 1.413-.877 2.485-.996 1.206-.134 2.262.034 2.944.765.05.053.096.108.139.165.044-.057.094-.112.143-.165.682-.731 1.738-.899 2.944-.765 1.23.137 2.145.528 2.724 1.261.566.715.693 1.614.693 2.484 0 .572-.053 1.148-.254 1.656.066.228.098.429.126.612.012.076.024.148.037.218.924.385 1.522 1.471 1.591 2.095Zm-5.083-8.707c-1.044-.116-1.488.091-1.681.297-.204.219-.359.679-.242 1.614.091.726.303 1.231.618 1.553.299.305.784.54 1.638.54.922 0 1.28-.198 1.442-.379.179-.2.308-.578.308-1.371 0-.765-.123-1.242-.37-1.554-.233-.296-.693-.587-1.713-.7Zm2.511 11.074c-1.393.776-3.272 1.428-5.43 1.428-4.562 0-7.873-2.914-7.998-3.749V9.338c.085-.628.677-1.686 1.588-2.065.013-.07.024-.143.036-.218.029-.183.06-.384.126-.612-.18-.455-.241-.963-.252-1.475L.31 4.107A.747.747 0 0 1 0 3.509V3.49a.748.748 0 0 1 .625-.73c.156-.026.306.047.435.139l14.667 10.578a.592.592 0 0 1 .227.264.752.752 0 0 1 .046.249v.022a.75.75 0 0 1-1.19.596Zm-1.367-.991L5.635 7.964a5.128 5.128 0 0 1-.889.073c-.652 0-1.236-.081-1.727-.291l-.023.116v4.255c.419.323 2.722 1.433 5.002 1.433 1.539 0 3.089-.505 4.063-.934Z"></path>
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</template>
<template id="workflow-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-workflow">
<path d="M0 1.75C0 .784.784 0 1.75 0h3.5C6.216 0 7 .784 7 1.75v3.5A1.75 1.75 0 0 1 5.25 7H4v4a1 1 0 0 0 1 1h4v-1.25C9 9.784 9.784 9 10.75 9h3.5c.966 0 1.75.784 1.75 1.75v3.5A1.75 1.75 0 0 1 14.25 16h-3.5A1.75 1.75 0 0 1 9 14.25v-.75H5A2.5 2.5 0 0 1 2.5 11V7h-.75A1.75 1.75 0 0 1 0 5.25Zm1.75-.25a.25.25 0 0 0-.25.25v3.5c0 .138.112.25.25.25h3.5a.25.25 0 0 0 .25-.25v-3.5a.25.25 0 0 0-.25-.25Zm9 9a.25.25 0 0 0-.25.25v3.5c0 .138.112.25.25.25h3.5a.25.25 0 0 0 .25-.25v-3.5a.25.25 0 0 0-.25-.25Z"></path>
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</template>
<template id="book-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-book">
<path d="M0 1.75A.75.75 0 0 1 .75 1h4.253c1.227 0 2.317.59 3 1.501A3.743 3.743 0 0 1 11.006 1h4.245a.75.75 0 0 1 .75.75v10.5a.75.75 0 0 1-.75.75h-4.507a2.25 2.25 0 0 0-1.591.659l-.622.621a.75.75 0 0 1-1.06 0l-.622-.621A2.25 2.25 0 0 0 5.258 13H.75a.75.75 0 0 1-.75-.75Zm7.251 10.324.004-5.073-.002-2.253A2.25 2.25 0 0 0 5.003 2.5H1.5v9h3.757a3.75 3.75 0 0 1 1.994.574ZM8.755 4.75l-.004 7.322a3.752 3.752 0 0 1 1.992-.572H14.5v-9h-3.495a2.25 2.25 0 0 0-2.25 2.25Z"></path>
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</template>
<template id="code-review-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-code-review">
<path d="M1.75 1h12.5c.966 0 1.75.784 1.75 1.75v8.5A1.75 1.75 0 0 1 14.25 13H8.061l-2.574 2.573A1.458 1.458 0 0 1 3 14.543V13H1.75A1.75 1.75 0 0 1 0 11.25v-8.5C0 1.784.784 1 1.75 1ZM1.5 2.75v8.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h6.5a.25.25 0 0 0 .25-.25v-8.5a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Zm5.28 1.72a.75.75 0 0 1 0 1.06L5.31 7l1.47 1.47a.751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018l-2-2a.75.75 0 0 1 0-1.06l2-2a.75.75 0 0 1 1.06 0Zm2.44 0a.75.75 0 0 1 1.06 0l2 2a.75.75 0 0 1 0 1.06l-2 2a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L10.69 7 9.22 5.53a.75.75 0 0 1 0-1.06Z"></path>
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</template>
<template id="codespaces-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-codespaces">
<path d="M0 11.25c0-.966.784-1.75 1.75-1.75h12.5c.966 0 1.75.784 1.75 1.75v3A1.75 1.75 0 0 1 14.25 16H1.75A1.75 1.75 0 0 1 0 14.25Zm2-9.5C2 .784 2.784 0 3.75 0h8.5C13.216 0 14 .784 14 1.75v5a1.75 1.75 0 0 1-1.75 1.75h-8.5A1.75 1.75 0 0 1 2 6.75Zm1.75-.25a.25.25 0 0 0-.25.25v5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-5a.25.25 0 0 0-.25-.25Zm-2 9.5a.25.25 0 0 0-.25.25v3c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25v-3a.25.25 0 0 0-.25-.25Z"></path><path d="M7 12.75a.75.75 0 0 1 .75-.75h4.5a.75.75 0 0 1 0 1.5h-4.5a.75.75 0 0 1-.75-.75Zm-4 0a.75.75 0 0 1 .75-.75h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1-.75-.75Z"></path>
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<template id="comment-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-comment">
<path d="M1 2.75C1 1.784 1.784 1 2.75 1h10.5c.966 0 1.75.784 1.75 1.75v7.5A1.75 1.75 0 0 1 13.25 12H9.06l-2.573 2.573A1.458 1.458 0 0 1 4 13.543V12H2.75A1.75 1.75 0 0 1 1 10.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h4.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path>
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<template id="comment-discussion-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-comment-discussion">
<path d="M1.75 1h8.5c.966 0 1.75.784 1.75 1.75v5.5A1.75 1.75 0 0 1 10.25 10H7.061l-2.574 2.573A1.458 1.458 0 0 1 2 11.543V10h-.25A1.75 1.75 0 0 1 0 8.25v-5.5C0 1.784.784 1 1.75 1ZM1.5 2.75v5.5c0 .138.112.25.25.25h1a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h3.5a.25.25 0 0 0 .25-.25v-5.5a.25.25 0 0 0-.25-.25h-8.5a.25.25 0 0 0-.25.25Zm13 2a.25.25 0 0 0-.25-.25h-.5a.75.75 0 0 1 0-1.5h.5c.966 0 1.75.784 1.75 1.75v5.5A1.75 1.75 0 0 1 14.25 12H14v1.543a1.458 1.458 0 0 1-2.487 1.03L9.22 12.28a.749.749 0 0 1 .326-1.275.749.749 0 0 1 .734.215l2.22 2.22v-2.19a.75.75 0 0 1 .75-.75h1a.25.25 0 0 0 .25-.25Z"></path>
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<template id="organization-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-organization">
<path d="M1.75 16A1.75 1.75 0 0 1 0 14.25V1.75C0 .784.784 0 1.75 0h8.5C11.216 0 12 .784 12 1.75v12.5c0 .085-.006.168-.018.25h2.268a.25.25 0 0 0 .25-.25V8.285a.25.25 0 0 0-.111-.208l-1.055-.703a.749.749 0 1 1 .832-1.248l1.055.703c.487.325.779.871.779 1.456v5.965A1.75 1.75 0 0 1 14.25 16h-3.5a.766.766 0 0 1-.197-.026c-.099.017-.2.026-.303.026h-3a.75.75 0 0 1-.75-.75V14h-1v1.25a.75.75 0 0 1-.75.75Zm-.25-1.75c0 .138.112.25.25.25H4v-1.25a.75.75 0 0 1 .75-.75h2.5a.75.75 0 0 1 .75.75v1.25h2.25a.25.25 0 0 0 .25-.25V1.75a.25.25 0 0 0-.25-.25h-8.5a.25.25 0 0 0-.25.25ZM3.75 6h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1 0-1.5ZM3 3.75A.75.75 0 0 1 3.75 3h.5a.75.75 0 0 1 0 1.5h-.5A.75.75 0 0 1 3 3.75Zm4 3A.75.75 0 0 1 7.75 6h.5a.75.75 0 0 1 0 1.5h-.5A.75.75 0 0 1 7 6.75ZM7.75 3h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1 0-1.5ZM3 9.75A.75.75 0 0 1 3.75 9h.5a.75.75 0 0 1 0 1.5h-.5A.75.75 0 0 1 3 9.75ZM7.75 9h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1 0-1.5Z"></path>
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<template id="rocket-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-rocket">
<path d="M14.064 0h.186C15.216 0 16 .784 16 1.75v.186a8.752 8.752 0 0 1-2.564 6.186l-.458.459c-.314.314-.641.616-.979.904v3.207c0 .608-.315 1.172-.833 1.49l-2.774 1.707a.749.749 0 0 1-1.11-.418l-.954-3.102a1.214 1.214 0 0 1-.145-.125L3.754 9.816a1.218 1.218 0 0 1-.124-.145L.528 8.717a.749.749 0 0 1-.418-1.11l1.71-2.774A1.748 1.748 0 0 1 3.31 4h3.204c.288-.338.59-.665.904-.979l.459-.458A8.749 8.749 0 0 1 14.064 0ZM8.938 3.623h-.002l-.458.458c-.76.76-1.437 1.598-2.02 2.5l-1.5 2.317 2.143 2.143 2.317-1.5c.902-.583 1.74-1.26 2.499-2.02l.459-.458a7.25 7.25 0 0 0 2.123-5.127V1.75a.25.25 0 0 0-.25-.25h-.186a7.249 7.249 0 0 0-5.125 2.123ZM3.56 14.56c-.732.732-2.334 1.045-3.005 1.148a.234.234 0 0 1-.201-.064.234.234 0 0 1-.064-.201c.103-.671.416-2.273 1.15-3.003a1.502 1.502 0 1 1 2.12 2.12Zm6.94-3.935c-.088.06-.177.118-.266.175l-2.35 1.521.548 1.783 1.949-1.2a.25.25 0 0 0 .119-.213ZM3.678 8.116 5.2 5.766c.058-.09.117-.178.176-.266H3.309a.25.25 0 0 0-.213.119l-1.2 1.95ZM12 5a1 1 0 1 1-2 0 1 1 0 0 1 2 0Z"></path>
</svg>
</template>
<template id="shield-check-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-shield-check">
<path d="m8.533.133 5.25 1.68A1.75 1.75 0 0 1 15 3.48V7c0 1.566-.32 3.182-1.303 4.682-.983 1.498-2.585 2.813-5.032 3.855a1.697 1.697 0 0 1-1.33 0c-2.447-1.042-4.049-2.357-5.032-3.855C1.32 10.182 1 8.566 1 7V3.48a1.75 1.75 0 0 1 1.217-1.667l5.25-1.68a1.748 1.748 0 0 1 1.066 0Zm-.61 1.429.001.001-5.25 1.68a.251.251 0 0 0-.174.237V7c0 1.36.275 2.666 1.057 3.859.784 1.194 2.121 2.342 4.366 3.298a.196.196 0 0 0 .154 0c2.245-.957 3.582-2.103 4.366-3.297C13.225 9.666 13.5 8.358 13.5 7V3.48a.25.25 0 0 0-.174-.238l-5.25-1.68a.25.25 0 0 0-.153 0ZM11.28 6.28l-3.5 3.5a.75.75 0 0 1-1.06 0l-1.5-1.5a.749.749 0 0 1 .326-1.275.749.749 0 0 1 .734.215l.97.97 2.97-2.97a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042Z"></path>
</svg>
</template>
<template id="heart-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-heart">
<path d="m8 14.25.345.666a.75.75 0 0 1-.69 0l-.008-.004-.018-.01a7.152 7.152 0 0 1-.31-.17 22.055 22.055 0 0 1-3.434-2.414C2.045 10.731 0 8.35 0 5.5 0 2.836 2.086 1 4.25 1 5.797 1 7.153 1.802 8 3.02 8.847 1.802 10.203 1 11.75 1 13.914 1 16 2.836 16 5.5c0 2.85-2.045 5.231-3.885 6.818a22.066 22.066 0 0 1-3.744 2.584l-.018.01-.006.003h-.002ZM4.25 2.5c-1.336 0-2.75 1.164-2.75 3 0 2.15 1.58 4.144 3.365 5.682A20.58 20.58 0 0 0 8 13.393a20.58 20.58 0 0 0 3.135-2.211C12.92 9.644 14.5 7.65 14.5 5.5c0-1.836-1.414-3-2.75-3-1.373 0-2.609.986-3.029 2.456a.749.749 0 0 1-1.442 0C6.859 3.486 5.623 2.5 4.25 2.5Z"></path>
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</template>
<template id="server-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-server">
<path d="M1.75 1h12.5c.966 0 1.75.784 1.75 1.75v4c0 .372-.116.717-.314 1 .198.283.314.628.314 1v4a1.75 1.75 0 0 1-1.75 1.75H1.75A1.75 1.75 0 0 1 0 12.75v-4c0-.358.109-.707.314-1a1.739 1.739 0 0 1-.314-1v-4C0 1.784.784 1 1.75 1ZM1.5 2.75v4c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25v-4a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Zm.25 5.75a.25.25 0 0 0-.25.25v4c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25v-4a.25.25 0 0 0-.25-.25ZM7 4.75A.75.75 0 0 1 7.75 4h4.5a.75.75 0 0 1 0 1.5h-4.5A.75.75 0 0 1 7 4.75ZM7.75 10h4.5a.75.75 0 0 1 0 1.5h-4.5a.75.75 0 0 1 0-1.5ZM3 4.75A.75.75 0 0 1 3.75 4h.5a.75.75 0 0 1 0 1.5h-.5A.75.75 0 0 1 3 4.75ZM3.75 10h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1 0-1.5Z"></path>
</svg>
</template>
<template id="globe-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-globe">
<path d="M8 0a8 8 0 1 1 0 16A8 8 0 0 1 8 0ZM5.78 8.75a9.64 9.64 0 0 0 1.363 4.177c.255.426.542.832.857 1.215.245-.296.551-.705.857-1.215A9.64 9.64 0 0 0 10.22 8.75Zm4.44-1.5a9.64 9.64 0 0 0-1.363-4.177c-.307-.51-.612-.919-.857-1.215a9.927 9.927 0 0 0-.857 1.215A9.64 9.64 0 0 0 5.78 7.25Zm-5.944 1.5H1.543a6.507 6.507 0 0 0 4.666 5.5c-.123-.181-.24-.365-.352-.552-.715-1.192-1.437-2.874-1.581-4.948Zm-2.733-1.5h2.733c.144-2.074.866-3.756 1.58-4.948.12-.197.237-.381.353-.552a6.507 6.507 0 0 0-4.666 5.5Zm10.181 1.5c-.144 2.074-.866 3.756-1.58 4.948-.12.197-.237.381-.353.552a6.507 6.507 0 0 0 4.666-5.5Zm2.733-1.5a6.507 6.507 0 0 0-4.666-5.5c.123.181.24.365.353.552.714 1.192 1.436 2.874 1.58 4.948Z"></path>
</svg>
</template>
<template id="issue-opened-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-issue-opened">
<path d="M8 9.5a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Z"></path><path d="M8 0a8 8 0 1 1 0 16A8 8 0 0 1 8 0ZM1.5 8a6.5 6.5 0 1 0 13 0 6.5 6.5 0 0 0-13 0Z"></path>
</svg>
</template>
<template id="device-mobile-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-device-mobile">
<path d="M3.75 0h8.5C13.216 0 14 .784 14 1.75v12.5A1.75 1.75 0 0 1 12.25 16h-8.5A1.75 1.75 0 0 1 2 14.25V1.75C2 .784 2.784 0 3.75 0ZM3.5 1.75v12.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25V1.75a.25.25 0 0 0-.25-.25h-8.5a.25.25 0 0 0-.25.25ZM8 13a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path>
</svg>
</template>
<template id="package-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-package">
<path d="m8.878.392 5.25 3.045c.54.314.872.89.872 1.514v6.098a1.75 1.75 0 0 1-.872 1.514l-5.25 3.045a1.75 1.75 0 0 1-1.756 0l-5.25-3.045A1.75 1.75 0 0 1 1 11.049V4.951c0-.624.332-1.201.872-1.514L7.122.392a1.75 1.75 0 0 1 1.756 0ZM7.875 1.69l-4.63 2.685L8 7.133l4.755-2.758-4.63-2.685a.248.248 0 0 0-.25 0ZM2.5 5.677v5.372c0 .09.047.171.125.216l4.625 2.683V8.432Zm6.25 8.271 4.625-2.683a.25.25 0 0 0 .125-.216V5.677L8.75 8.432Z"></path>
</svg>
</template>
<template id="credit-card-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-credit-card">
<path d="M10.75 9a.75.75 0 0 0 0 1.5h1.5a.75.75 0 0 0 0-1.5h-1.5Z"></path><path d="M0 3.75C0 2.784.784 2 1.75 2h12.5c.966 0 1.75.784 1.75 1.75v8.5A1.75 1.75 0 0 1 14.25 14H1.75A1.75 1.75 0 0 1 0 12.25ZM14.5 6.5h-13v5.75c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25Zm0-2.75a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25V5h13Z"></path>
</svg>
</template>
<template id="play-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-play">
<path d="M8 0a8 8 0 1 1 0 16A8 8 0 0 1 8 0ZM1.5 8a6.5 6.5 0 1 0 13 0 6.5 6.5 0 0 0-13 0Zm4.879-2.773 4.264 2.559a.25.25 0 0 1 0 .428l-4.264 2.559A.25.25 0 0 1 6 10.559V5.442a.25.25 0 0 1 .379-.215Z"></path>
</svg>
</template>
<template id="gift-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-gift">
<path d="M2 2.75A2.75 2.75 0 0 1 4.75 0c.983 0 1.873.42 2.57 1.232.268.318.497.668.68 1.042.183-.375.411-.725.68-1.044C9.376.42 10.266 0 11.25 0a2.75 2.75 0 0 1 2.45 4h.55c.966 0 1.75.784 1.75 1.75v2c0 .698-.409 1.301-1 1.582v4.918A1.75 1.75 0 0 1 13.25 16H2.75A1.75 1.75 0 0 1 1 14.25V9.332C.409 9.05 0 8.448 0 7.75v-2C0 4.784.784 4 1.75 4h.55c-.192-.375-.3-.8-.3-1.25ZM7.25 9.5H2.5v4.75c0 .138.112.25.25.25h4.5Zm1.5 0v5h4.5a.25.25 0 0 0 .25-.25V9.5Zm0-4V8h5.5a.25.25 0 0 0 .25-.25v-2a.25.25 0 0 0-.25-.25Zm-7 0a.25.25 0 0 0-.25.25v2c0 .138.112.25.25.25h5.5V5.5h-5.5Zm3-4a1.25 1.25 0 0 0 0 2.5h2.309c-.233-.818-.542-1.401-.878-1.793-.43-.502-.915-.707-1.431-.707ZM8.941 4h2.309a1.25 1.25 0 0 0 0-2.5c-.516 0-1 .205-1.43.707-.337.392-.646.975-.879 1.793Z"></path>
</svg>
</template>
<template id="code-square-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-code-square">
<path d="M0 1.75C0 .784.784 0 1.75 0h12.5C15.216 0 16 .784 16 1.75v12.5A1.75 1.75 0 0 1 14.25 16H1.75A1.75 1.75 0 0 1 0 14.25Zm1.75-.25a.25.25 0 0 0-.25.25v12.5c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25V1.75a.25.25 0 0 0-.25-.25Zm7.47 3.97a.75.75 0 0 1 1.06 0l2 2a.75.75 0 0 1 0 1.06l-2 2a.749.749 0 0 1-1.275-.326.749.749 0 0 1 .215-.734L10.69 8 9.22 6.53a.75.75 0 0 1 0-1.06ZM6.78 6.53 5.31 8l1.47 1.47a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215l-2-2a.75.75 0 0 1 0-1.06l2-2a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042Z"></path>
</svg>
</template>
<template id="device-desktop-icon">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-device-desktop">
<path d="M14.25 1c.966 0 1.75.784 1.75 1.75v7.5A1.75 1.75 0 0 1 14.25 12h-3.727c.099 1.041.52 1.872 1.292 2.757A.752.752 0 0 1 11.25 16h-6.5a.75.75 0 0 1-.565-1.243c.772-.885 1.192-1.716 1.292-2.757H1.75A1.75 1.75 0 0 1 0 10.25v-7.5C0 1.784.784 1 1.75 1ZM1.75 2.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h12.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25ZM9.018 12H6.982a5.72 5.72 0 0 1-.765 2.5h3.566a5.72 5.72 0 0 1-.765-2.5Z"></path>
</svg>
</template>
<div class="position-relative">
<ul
role="listbox"
class="ActionListWrap QueryBuilder-ListWrap"
aria-label="Suggestions"
data-action="
combobox-commit:query-builder#comboboxCommit
mousedown:query-builder#resultsMousedown
"
data-target="query-builder.resultsList"
data-persist-list=false
id="query-builder-test-results"
></ul>
</div>
<div class="FormControl-inlineValidation" id="validation-58c1b225-84f7-45e1-a93b-22fe636f360f" hidden="hidden">
<span class="FormControl-inlineValidation--visual">
<svg aria-hidden="true" height="12" viewBox="0 0 12 12" version="1.1" width="12" data-view-component="true" class="octicon octicon-alert-fill">
<path d="M4.855.708c.5-.896 1.79-.896 2.29 0l4.675 8.351a1.312 1.312 0 0 1-1.146 1.954H1.33A1.313 1.313 0 0 1 .183 9.058ZM7 7V3H5v4Zm-1 3a1 1 0 1 0 0-2 1 1 0 0 0 0 2Z"></path>
</svg>
</span>
<span></span>
</div> </div>
<div data-target="query-builder.screenReaderFeedback" aria-live="polite" aria-atomic="true" class="sr-only"></div>
</query-builder></form>
<div class="d-flex flex-row color-fg-muted px-3 text-small color-bg-default search-feedback-prompt">
<a target="_blank" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax" data-view-component="true" class="Link color-fg-accent text-normal ml-2">Search syntax tips</a> <div class="d-flex flex-1"></div>
</div>
</div>
</div>
</div>
</modal-dialog></div>
</div>
<div data-action="click:qbsearch-input#retract" class="dark-backdrop position-fixed" hidden data-target="qbsearch-input.darkBackdrop"></div>
<div class="color-fg-default">
<dialog-helper>
<dialog data-target="qbsearch-input.feedbackDialog" data-action="close:qbsearch-input#handleDialogClose cancel:qbsearch-input#handleDialogClose" id="feedback-dialog" aria-modal="true" aria-labelledby="feedback-dialog-title" aria-describedby="feedback-dialog-description" data-view-component="true" class="Overlay Overlay-whenNarrow Overlay--size-medium Overlay--motion-scaleFade Overlay--disableScroll">
<div data-view-component="true" class="Overlay-header">
<div class="Overlay-headerContentWrap">
<div class="Overlay-titleWrap">
<h1 class="Overlay-title " id="feedback-dialog-title">
Provide feedback
</h1>
</div>
<div class="Overlay-actionWrap">
<button data-close-dialog-id="feedback-dialog" aria-label="Close" aria-label="Close" type="button" data-view-component="true" class="close-button Overlay-closeButton"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x">
<path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path>
</svg></button>
</div>
</div>
</div>
<scrollable-region data-labelled-by="feedback-dialog-title">
<div data-view-component="true" class="Overlay-body"> <!-- '"` --><!-- </textarea></xmp> --></option></form><form id="code-search-feedback-form" data-turbo="false" action="/search/feedback" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="fSGzwiVUr+fJt3KBWILdh6Tc+RaAzSyyMXYlYaXn5WNgzAKWT6XwaxIKcpcNlIRxgZbVUL162pzTF1gUzIJ8aQ==" />
<p>We read every piece of feedback, and take your input very seriously.</p>
<textarea name="feedback" class="form-control width-full mb-2" style="height: 120px" id="feedback"></textarea>
<input name="include_email" id="include_email" aria-label="Include my email address so I can be contacted" class="form-control mr-2" type="checkbox">
<label for="include_email" style="font-weight: normal">Include my email address so I can be contacted</label>
</form></div>
</scrollable-region>
<div data-view-component="true" class="Overlay-footer Overlay-footer--alignEnd"> <button data-close-dialog-id="feedback-dialog" type="button" data-view-component="true" class="btn"> Cancel
</button>
<button form="code-search-feedback-form" data-action="click:qbsearch-input#submitFeedback" type="submit" data-view-component="true" class="btn-primary btn"> Submit feedback
</button>
</div>
</dialog></dialog-helper>
<custom-scopes data-target="qbsearch-input.customScopesManager">
<dialog-helper>
<dialog data-target="custom-scopes.customScopesModalDialog" data-action="close:qbsearch-input#handleDialogClose cancel:qbsearch-input#handleDialogClose" id="custom-scopes-dialog" aria-modal="true" aria-labelledby="custom-scopes-dialog-title" aria-describedby="custom-scopes-dialog-description" data-view-component="true" class="Overlay Overlay-whenNarrow Overlay--size-medium Overlay--motion-scaleFade Overlay--disableScroll">
<div data-view-component="true" class="Overlay-header Overlay-header--divided">
<div class="Overlay-headerContentWrap">
<div class="Overlay-titleWrap">
<h1 class="Overlay-title " id="custom-scopes-dialog-title">
Saved searches
</h1>
<h2 id="custom-scopes-dialog-description" class="Overlay-description">Use saved searches to filter your results more quickly</h2>
</div>
<div class="Overlay-actionWrap">
<button data-close-dialog-id="custom-scopes-dialog" aria-label="Close" aria-label="Close" type="button" data-view-component="true" class="close-button Overlay-closeButton"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x">
<path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path>
</svg></button>
</div>
</div>
</div>
<scrollable-region data-labelled-by="custom-scopes-dialog-title">
<div data-view-component="true" class="Overlay-body"> <div data-target="custom-scopes.customScopesModalDialogFlash"></div>
<div hidden class="create-custom-scope-form" data-target="custom-scopes.createCustomScopeForm">
<!-- '"` --><!-- </textarea></xmp> --></option></form><form id="custom-scopes-dialog-form" data-turbo="false" action="/search/custom_scopes" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="2GrrxbR96gOkRrYubQLRNOmrrj0n4a+z/0mO/30aDqcqo9zUs+16ZLVnIKH0D1z1H0M7/1L7fZtsAc8pJveZgQ==" />
<div data-target="custom-scopes.customScopesModalDialogFlash"></div>
<input type="hidden" id="custom_scope_id" name="custom_scope_id" data-target="custom-scopes.customScopesIdField">
<div class="form-group">
<label for="custom_scope_name">Name</label>
<auto-check src="/search/custom_scopes/check_name" required only-validate-on-blur="false">
<input
type="text"
name="custom_scope_name"
id="custom_scope_name"
data-target="custom-scopes.customScopesNameField"
class="form-control"
autocomplete="off"
placeholder="github-ruby"
required
maxlength="50">
<input type="hidden" data-csrf="true" value="nfGqUq1WNFaMHapu6Eka16roBldSA+R3bDM346sq9d5nXOBJ1Cf9Yqiqo2i0uv1EMwFOHxelOeHUvnmzwoYgOw==" />
</auto-check>
</div>
<div class="form-group">
<label for="custom_scope_query">Query</label>
<input
type="text"
name="custom_scope_query"
id="custom_scope_query"
data-target="custom-scopes.customScopesQueryField"
class="form-control"
autocomplete="off"
placeholder="(repo:mona/a OR repo:mona/b) AND lang:python"
required
maxlength="500">
</div>
<p class="text-small color-fg-muted">
To see all available qualifiers, see our <a class="Link--inTextBlock" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax">documentation</a>.
</p>
</form> </div>
<div data-target="custom-scopes.manageCustomScopesForm">
<div data-target="custom-scopes.list"></div>
</div>
</div>
</scrollable-region>
<div data-view-component="true" class="Overlay-footer Overlay-footer--alignEnd Overlay-footer--divided"> <button data-action="click:custom-scopes#customScopesCancel" type="button" data-view-component="true" class="btn"> Cancel
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Python implementation of Bayesian Knowledge Tracing and extensions
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<script type="application/json" data-target="react-partial.embeddedData">{"props":{"initialPayload":{"allShortcutsEnabled":false,"path":"/","repo":{"id":92357546,"defaultBranch":"master","name":"pyBKT","ownerLogin":"CAHLR","currentUserCanPush":false,"isFork":false,"isEmpty":false,"createdAt":"2017-05-25T02:42:08.000Z","ownerAvatar":"https://avatars.githubusercontent.com/u/10409555?v=4","public":true,"private":false,"isOrgOwned":true},"currentUser":null,"refInfo":{"name":"master","listCacheKey":"v0:1688792031.0","canEdit":false,"refType":"branch","currentOid":"6c0f7a19a811ed60b87e034cb2d436503a6ef20b"},"tree":{"items":[{"name":"source-cpp/pyBKT","path":"source-cpp/pyBKT","contentType":"directory","hasSimplifiedPath":true},{"name":"source-py/pyBKT","path":"source-py/pyBKT","contentType":"directory","hasSimplifiedPath":true},{"name":".gitignore","path":".gitignore","contentType":"file"},{"name":"LICENSE","path":"LICENSE","contentType":"file"},{"name":"MANIFEST.in","path":"MANIFEST.in","contentType":"file"},{"name":"README.md","path":"README.md","contentType":"file"},{"name":"setup.cfg","path":"setup.cfg","contentType":"file"},{"name":"setup.py","path":"setup.py","contentType":"file"}],"templateDirectorySuggestionUrl":null,"readme":null,"totalCount":8,"showBranchInfobar":false},"fileTree":null,"fileTreeProcessingTime":null,"foldersToFetch":[],"treeExpanded":false,"symbolsExpanded":false,"isOverview":true,"overview":{"banners":{"shouldRecommendReadme":false,"isPersonalRepo":false,"showUseActionBanner":false,"actionSlug":null,"actionId":null,"showProtectBranchBanner":false,"publishBannersInfo":{"dismissActionNoticePath":"/settings/dismiss-notice/publish_action_from_repo","releasePath":"/CAHLR/pyBKT/releases/new?marketplace=true","showPublishActionBanner":false},"interactionLimitBanner":null,"showInvitationBanner":false,"inviterName":null,"actionsMigrationBannerInfo":{"releaseTags":[],"showImmutableActionsMigrationBanner":false,"initialMigrationStatus":null}},"codeButton":{"contactPath":"/contact","isEnterprise":false,"local":{"protocolInfo":{"httpAvailable":true,"sshAvailable":null,"httpUrl":"https://github.com/CAHLR/pyBKT.git","showCloneWarning":null,"sshUrl":null,"sshCertificatesRequired":null,"sshCertificatesAvailable":null,"ghCliUrl":"gh repo clone CAHLR/pyBKT","defaultProtocol":"http","newSshKeyUrl":"/settings/ssh/new","setProtocolPath":"/users/set_protocol"},"platformInfo":{"cloneUrl":"https://desktop.github.com","showVisualStudioCloneButton":false,"visualStudioCloneUrl":"https://windows.github.com","showXcodeCloneButton":false,"xcodeCloneUrl":"xcode://clone?repo=https%3A%2F%2Fgithub.com%2FCAHLR%2FpyBKT","zipballUrl":"/CAHLR/pyBKT/archive/refs/heads/master.zip"}},"newCodespacePath":"/codespaces/new?hide_repo_select=true\u0026repo=92357546"},"popovers":{"rename":null,"renamedParentRepo":null},"commitCount":"368","overviewFiles":[{"displayName":"README.md","repoName":"pyBKT","refName":"master","path":"README.md","preferredFileType":"readme","tabName":"README","richText":"\u003carticle class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003epyBKT\u003c/h1\u003e\u003ca id=\"user-content-pybkt\" class=\"anchor\" aria-label=\"Permalink: pyBKT\" href=\"#pybkt\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePython implementation of the Bayesian Knowledge Tracing algorithm and variants, estimating student cognitive mastery from problem solving sequences.\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" pip install pyBKT\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e pip install pyBKT\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eBased on the work of Zachary A. Pardos (\u003ca href=\"mailto:[email protected]\"\[email protected]\u003c/a\u003e) and Matthew J. Johnson (\u003ca href=\"mailto:[email protected]\"\[email protected]\u003c/a\u003e) @ \u003ca href=\"https://github.com/CAHLR/xBKT\"\u003ehttps://github.com/CAHLR/xBKT\u003c/a\u003e. All-platform python adaptation and optimizations by Anirudhan Badrinath (\u003ca href=\"mailto:[email protected]\"\[email protected]\u003c/a\u003e). Data helpers and other utility functions written by Frederic Wang (\u003ca href=\"mailto:[email protected]\"\[email protected]\u003c/a\u003e). Original Python and boost adaptation of xBKT by Cristian Garay (\u003ca href=\"mailto:[email protected]\"\[email protected]\u003c/a\u003e). For implementation details, analysis of runtime and data requirements, and model variant replication testing, refer to:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBadrinath, A., Wang, F., Pardos, Z.A. (2021) \u003ca href=\"https://educationaldatamining.org/EDM2021/virtual/static/pdf/EDM21_paper_237.pdf\" rel=\"nofollow\"\u003epyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models\u003c/a\u003e. In S. Hsiao, \u0026amp; S. Sahebi (Eds.) \u003cem\u003eProceedings of the 14th International Conference on Educational Data Mining\u003c/em\u003e (EDM). Pages 468-474.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBulut, O., Shin, J., Yildirim-Erbasli, S. N., Gorgun, G., \u0026amp; Pardos, Z. A. (2023). \u003ca href=\"https://www.mdpi.com/2624-8611/5/3/50\" rel=\"nofollow\"\u003eAn introduction to Bayesian knowledge tracing with pyBKT\u003c/a\u003e. \u003cem\u003ePsych\u003c/em\u003e, 5(3), 770-786.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExamples from the paper can be found in \u003ca href=\"https://github.com/CAHLR/pyBKT-examples/\" title=\"pyBKT examples\"\u003epyBKT-examples\u003c/a\u003e repo.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://colab.research.google.com/drive/13abu919edUXbvPV3qeGPpvwnFBExU7Vd\" title=\"pyBKT quick start in Colab\" rel=\"nofollow\"\u003epyBKT Quick Start Tutorial\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://colab.research.google.com/drive/1Kg6AvXKdSZXoqzSZ5BRHuewyHRMvrZs1\" title=\"pyBKT quick start in Colab\" rel=\"nofollow\"\u003epyBKT Tutorial from LAK Workshop in Google Colab Notebook\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRequirements\u003c/h2\u003e\u003ca id=\"user-content-requirements\" class=\"anchor\" aria-label=\"Permalink: Requirements\" href=\"#requirements\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePython \u0026gt;= 3.5\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSupported OS: All platforms! (Yes, Windows too)\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSupported model variants\u003c/h2\u003e\u003ca id=\"user-content-supported-model-variants\" class=\"anchor\" aria-label=\"Permalink: Supported model variants\" href=\"#supported-model-variants\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003epyBKT can be used to define and fit many BKT variants, including these from the literature:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eIndividual student priors, learn rate, guess, and slip [1,2]\u003c/li\u003e\n\u003cli\u003eIndividual item guess and slip [3,4,5]\u003c/li\u003e\n\u003cli\u003eIndividual item or resource learn rate [4,5]\u003c/li\u003e\n\u003c/ul\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003ePardos, Z. A., Heffernan, N. T. (2010) Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing. In P. De Bra, A. Kobsa, D. Chin (Eds.) \u003cem\u003eProceedings of the 18th International Conference on User Modeling, Adaptation and Personalization\u003c/em\u003e (UMAP). Big Island of Hawaii. Pages. Springer. Pages 255-266. \u003ca href=\"https://doi.org/10.1007/978-3-642-13470-8_24\" rel=\"nofollow\"\u003e[doi]\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003ePardos, Z. A., Heffernan, N. T. (2010) Using HMMs and bagged decision trees to leverage rich features of user and skill from an intelligent tutoring system dataset. In J. Stamper \u0026amp; A. Niculescu-Mizil (Eds.) \u003cem\u003eProceedings of the KDD Cup Workshop at the 16th ACM Conference on Knowledge Discovery and Data Mining\u003c/em\u003e (SIGKDD). Washington, D.C. ACM. Pages 24-35. \u003ca href=\"https://pslcdatashop.web.cmu.edu/KDDCup/workshop/papers/pardos_heffernan_KDD_Cup_2010_article.pdf\" rel=\"nofollow\"\u003e[kdd cup]\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003ePardos, Z. \u0026amp; Heffernan, N. (2011) KT-IDEM: Introducing Item Difficulty to the Knowledge Tracing Model. In Konstant et al. (eds.) \u003cem\u003eProceedings of the 20th International Conference on User Modeling, Adaptation and Personalization\u003c/em\u003e (UMAP). Girona, Spain. Springer. Pages 243-254. \u003ca href=\"https://doi.org/10.1007/978-3-642-22362-4_21\" rel=\"nofollow\"\u003e[doi]\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003ePardos, Z. A., Bergner, Y., Seaton, D., Pritchard, D.E. (2013) Adapting Bayesian Knowledge Tracing to a Massive Open Online College Course in edX. In S.K. D’Mello, R.A. Calvo, \u0026amp; A. Olney (Eds.) \u003cem\u003eProceedings of the 6th International Conference on Educational Data Mining\u003c/em\u003e (EDM). Memphis, TN. Pages 137-144. \u003ca href=\"http://educationaldatamining.org/EDM2013/proceedings/paper_20.pdf\" rel=\"nofollow\"\u003e[edm]\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eXu, Y., Johnson, M. J., Pardos, Z. A. (2015) Scaling cognitive modeling to massive open environments. In \u003cem\u003eProceedings of the Workshop on Machine Learning for Education at the 32nd International Conference on Machine Learning\u003c/em\u003e (ICML). Lille, France. \u003ca href=\"http://ml4ed.cc/attachments/XuY.pdf\" rel=\"nofollow\"\u003e[icml ml4ed]\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInstallation and setup\u003c/h1\u003e\u003ca id=\"user-content-installation-and-setup\" class=\"anchor\" aria-label=\"Permalink: Installation and setup\" href=\"#installation-and-setup\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis is intended as a quick overview of steps to install and setup and to run pyBKT locally.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWe offer both a pure Python port and a Python/C++ extension version of pyBKT for the sake of accessibility and ease of use on any platform. Note that pip, by default, will install the C++/Python version unless the required libraries are not found or there is an error during installation. In the case of such issues, it will revert to the pure Python implementation.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe former pure Python versions does not fit models or scale as quickly or efficiently as the latter (due to nested for loops needed for DP). Here are a few speed comparisons - both on the same machine - that may be useful in deciding which version is more appropriate given the usage (e.g. model fitting is far more demanding than prediction).\u003c/p\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"center\"\u003eTest Description\u003c/th\u003e\n\u003cth align=\"center\"\u003epyBKT (Python)\u003c/th\u003e\n\u003cth align=\"right\"\u003epyBKT (C++)\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"center\"\u003esynthetic data, model fit (500 students)\u003c/td\u003e\n\u003ctd align=\"center\"\u003e~1m55s\u003c/td\u003e\n\u003ctd align=\"right\"\u003e~1.5s\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"center\"\u003esynthetic data, model fit (5000 students)\u003c/td\u003e\n\u003ctd align=\"center\"\u003e~1h30m\u003c/td\u003e\n\u003ctd align=\"right\"\u003e~45s\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"center\"\u003ecross validated cognitive tutor data\u003c/td\u003e\n\u003ctd align=\"center\"\u003e~4m10s\u003c/td\u003e\n\u003ctd align=\"right\"\u003e~3s\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"center\"\u003esynthetic data, predict onestep (500 students)\u003c/td\u003e\n\u003ctd align=\"center\"\u003e~2s\u003c/td\u003e\n\u003ctd align=\"right\"\u003e~0.8s\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"center\"\u003esynthetic data, predict onestep (5000 students)\u003c/td\u003e\n\u003ctd align=\"center\"\u003e~2m15s\u003c/td\u003e\n\u003ctd align=\"right\"\u003e~35s\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInstalling Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)\u003c/h2\u003e\u003ca id=\"user-content-installing-dependencies-for-fast-c-inferencing-optional---for-os-x-and-linux\" class=\"anchor\" aria-label=\"Permalink: Installing Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)\" href=\"#installing-dependencies-for-fast-c-inferencing-optional---for-os-x-and-linux\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNote: this section is not applicable for Windows as running the Python/C++ version is cumbersome and untested. For Windows, we only offer the slower, pure Python version of pyBKT (it will be installed automatically).\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eLinux\u003c/h3\u003e\u003ca id=\"user-content-linux\" class=\"anchor\" aria-label=\"Permalink: Linux\" href=\"#linux\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIf you have a C++ compiler already installed, pip will install pyBKT with fast C++ inferencing. C++ compilers are already installed on nearly all Linux distributions. If it is not installed on your machine, type \u003ccode\u003esudo apt install gcc g++\u003c/code\u003e if using Debian based distributions. Otherwise, whichever package manager is appropriately suited to your distribution (\u003ccode\u003ednf\u003c/code\u003e, \u003ccode\u003epacman\u003c/code\u003e, etc.). Without a compiler, pip will install pyBKT without C++ speed optimizations.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eMac\u003c/h3\u003e\u003ca id=\"user-content-mac\" class=\"anchor\" aria-label=\"Permalink: Mac\" href=\"#mac\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe latest version of Python is necessary for OS X. If homebrew is installed, run the following commands to download the necessary dependencies:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" brew install libomp\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e brew install libomp\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInstalling pyBKT\u003c/h2\u003e\u003ca id=\"user-content-installing-pybkt\" class=\"anchor\" aria-label=\"Permalink: Installing pyBKT\" href=\"#installing-pybkt\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can simply run:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" pip install pyBKT\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e pip install pyBKT\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAlternatively, if \u003ccode\u003epip\u003c/code\u003e poses some problems, you can clone the repository as such and then run the \u003ccode\u003esetup.py\u003c/code\u003e script manually.\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" git clone https://github.com/CAHLR/pyBKT.git\n cd pyBKT\n python3 setup.py install\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e git clone https://github.com/CAHLR/pyBKT.git\n cd pyBKT\n python3 setup.py install\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePreparing Data and Running Model\u003c/h1\u003e\u003ca id=\"user-content-preparing-data-and-running-model\" class=\"anchor\" aria-label=\"Permalink: Preparing Data and Running Model\" href=\"#preparing-data-and-running-model\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe following serves as a mini-tutorial for how to get started with pyBKT. There is more information available at the Colab notebook listed at the top of the README.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInput and Output Data\u003c/h2\u003e\u003ca id=\"user-content-input-and-output-data\" class=\"anchor\" aria-label=\"Permalink: Input and Output Data\" href=\"#input-and-output-data\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe accepted input formats are Pandas DataFrames and data files of type csv (comma separated) or tsv (tab separated). pyBKT will automatically infer which delimiter to use in the case that it is passed a data file. Since column names mapping meaning to each field in the data (i.e. skill name, correct/incorrect) vary per data source, you may need to specify a mapping from your data file's column names to pyBKT's expected column names. In many cases with Cognitive Tutor and Assistments datasets, pyBKT will be able to automatically infer column name mappings, but in the case that it is unable to, it will raise an exception. Note that the correctness is given by -1 (no response), 0 (incorrect), or 1 (correct).\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCreating and Training Models\u003c/h2\u003e\u003ca id=\"user-content-creating-and-training-models\" class=\"anchor\" aria-label=\"Permalink: Creating and Training Models\" href=\"#creating-and-training-models\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe process of creating and training models in pyBKT resemble that of SciKit Learn. pyBKT provides easy methods of fetching online datasets and to fit on a combination or all skills available in any particular dataset.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"from pyBKT.models import Model\n\n# Initialize the model with an optional seed\nmodel = Model(seed = 42, num_fits = 1)\n\n# Fetch Assistments and CognitiveTutor data (optional - if you have your own dataset, that's fine too!)\nmodel.fetch_dataset('https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/as.csv', '.')\nmodel.fetch_dataset('https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/ct.csv', '.')\n\n# Train a simple BKT model on all skills in the CT dataset\nmodel.fit(data_path = 'ct.csv')\n\n# Train a simple BKT model on one skill in the CT dataset\n# Note that calling fit deletes any previous trained BKT model!\nmodel.fit(data_path = 'ct.csv', skills = \u0026quot;Plot imperfect radical\u0026quot;)\n\n# Train a simple BKT model on multiple skills in the CT dataset\nmodel.fit(data_path = 'ct.csv', skills = [\u0026quot;Plot imperfect radical\u0026quot;,\n \u0026quot;Plot pi\u0026quot;])\n\n# Train a multiguess and slip BKT model on multiple skills in the\n# CT dataset. Note: if you are not using CognitiveTutor or Assistments\n# data, you may need to provide a column mapping for the guess/slip\n# classes to use (i.e. if the column name is gsclasses, you would\n# specify multigs = 'gsclasses' or specify a defaults dictionary\n# defaults = {'multigs': 'gsclasses'}).\nmodel.fit(data_path = 'ct.csv', skills = [\u0026quot;Plot imperfect radical\u0026quot;,\n \u0026quot;Plot pi\u0026quot;],\n multigs = True)\n\n# We can combine multiple model variants.\nmodel.fit(data_path = 'ct.csv', skills = [\u0026quot;Plot imperfect radical\u0026quot;,\n \u0026quot;Plot pi\u0026quot;],\n multigs = True, forgets = True,\n multilearn = True)\n\n# We can use a different column to specify the different learn and \n# forget classes. In this case, we use student ID.\nmodel.fit(data_path = 'ct.csv', skills = [\u0026quot;Plot imperfect radical\u0026quot;,\n \u0026quot;Plot pi\u0026quot;],\n multigs = True, forgets = True,\n multilearn = 'Anon Student Id')\n\n# View the trained parameters!\nprint(model.params())\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epyBKT\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003emodels\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eModel\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Initialize the model with an optional seed\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eModel\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eseed\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e42\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enum_fits\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Fetch Assistments and CognitiveTutor data (optional - if you have your own dataset, that's fine too!)\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efetch_dataset\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/as.csv'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'.'\u003c/span\u003e)\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efetch_dataset\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'.'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Train a simple BKT model on all skills in the CT dataset\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Train a simple BKT model on one skill in the CT dataset\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# Note that calling fit deletes any previous trained BKT model!\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"Plot imperfect radical\"\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Train a simple BKT model on multiple skills in the CT dataset\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e [\u003cspan class=\"pl-s\"\u003e\"Plot imperfect radical\"\u003c/span\u003e,\n \u003cspan class=\"pl-s\"\u003e\"Plot pi\"\u003c/span\u003e])\n\n\u003cspan class=\"pl-c\"\u003e# Train a multiguess and slip BKT model on multiple skills in the\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# CT dataset. Note: if you are not using CognitiveTutor or Assistments\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# data, you may need to provide a column mapping for the guess/slip\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# classes to use (i.e. if the column name is gsclasses, you would\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# specify multigs = 'gsclasses' or specify a defaults dictionary\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# defaults = {'multigs': 'gsclasses'}).\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e [\u003cspan class=\"pl-s\"\u003e\"Plot imperfect radical\"\u003c/span\u003e,\n \u003cspan class=\"pl-s\"\u003e\"Plot pi\"\u003c/span\u003e],\n \u003cspan class=\"pl-s1\"\u003emultigs\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# We can combine multiple model variants.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e [\u003cspan class=\"pl-s\"\u003e\"Plot imperfect radical\"\u003c/span\u003e,\n \u003cspan class=\"pl-s\"\u003e\"Plot pi\"\u003c/span\u003e],\n \u003cspan class=\"pl-s1\"\u003emultigs\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eforgets\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e,\n \u003cspan class=\"pl-s1\"\u003emultilearn\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# We can use a different column to specify the different learn and \u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# forget classes. In this case, we use student ID.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e [\u003cspan class=\"pl-s\"\u003e\"Plot imperfect radical\"\u003c/span\u003e,\n \u003cspan class=\"pl-s\"\u003e\"Plot pi\"\u003c/span\u003e],\n \u003cspan class=\"pl-s1\"\u003emultigs\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eforgets\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e,\n \u003cspan class=\"pl-s1\"\u003emultilearn\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'Anon Student Id'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# View the trained parameters!\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eparams\u003c/span\u003e())\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNote that if we train on a dataset that has unfamiliar columns to pyBKT, you will be required to specify a mapping of column names in that dataset to expected pyBKT columns. This is referred to as the model defaults (i.e. it specifies the default column names to lookup in the dataset). An example usage is provided below for an unknown dataset which has column names \"row\", \"skill_t\", \"answer\", and \"gs_classes\".\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"# Load unfamiliar dataset.\ndf = pd.read_csv('mystery.csv')\n\n# For other non-Assistments/CogTutor style datasets, we will need to specify the\n# columns corresponding to each required column (i.e. the user ID, correct/incorrect).\n# For that, we use a defaults dictionary.\n# In this case, the order ID that pyBKT expects is specified by the column row in the\n# dataset, the skill_name is specified by a column skill_t and the correctness is specified\n# by the answer column in the dataset.\ndefaults = {'order_id': 'row', 'skill_name': 'skill_t', 'correct': 'answer'}\n\n# This defaults dictionary contains columns specifying what columns correspond\n# to the desired guess/slip classes, etc. In this case, our desired column for\n# the guess/slip classes is a column named gs_classes.\ndefaults['multigs'] = 'gs_classes'\n\n# Fit using the defaults (column mappings) specified in the dictionary.\nmodel.fit(data = df, defaults = defaults)\n\n# Predict/evaluate/etc.\ntraining_acc = model.evaluate(data = df, metric = 'accuracy')\"\u003e\u003cpre\u003e\u003cspan class=\"pl-c\"\u003e# Load unfamiliar dataset.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003edf\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epd\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eread_csv\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'mystery.csv'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# For other non-Assistments/CogTutor style datasets, we will need to specify the\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# columns corresponding to each required column (i.e. the user ID, correct/incorrect).\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# For that, we use a defaults dictionary.\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# In this case, the order ID that pyBKT expects is specified by the column row in the\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# dataset, the skill_name is specified by a column skill_t and the correctness is specified\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# by the answer column in the dataset.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003edefaults\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e {\u003cspan class=\"pl-s\"\u003e'order_id'\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e'row'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'skill_name'\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e'skill_t'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'correct'\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e'answer'\u003c/span\u003e}\n\n\u003cspan class=\"pl-c\"\u003e# This defaults dictionary contains columns specifying what columns correspond\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# to the desired guess/slip classes, etc. In this case, our desired column for\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# the guess/slip classes is a column named gs_classes.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003edefaults\u003c/span\u003e[\u003cspan class=\"pl-s\"\u003e'multigs'\u003c/span\u003e] \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'gs_classes'\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Fit using the defaults (column mappings) specified in the dictionary.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003edf\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003edefaults\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003edefaults\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Predict/evaluate/etc.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003etraining_acc\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eevaluate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003edf\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emetric\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'accuracy'\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eModel Prediction and Evaluation\u003c/h2\u003e\u003ca id=\"user-content-model-prediction-and-evaluation\" class=\"anchor\" aria-label=\"Permalink: Model Prediction and Evaluation\" href=\"#model-prediction-and-evaluation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePrediction and evaluation behave similarly to SciKit-Learn. pyBKT offers a variety of features for prediction and evaluation.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"from pyBKT.models import Model\n\n# Initialize the model with an optional seed\nmodel = Model(seed = 42, num_fits = 1)\n\n# Load the Cognitive Tutor data (not necessary, but shown\n# for the purposes of the tutorial that pyBKT accepts\n# DataFrames as well as file locations!).\nct_df = pd.read_csv('ct.csv', encoding = 'latin')\n\n# Train a simple BKT model on all skills in the CT dataset\nmodel.fit(data_path = 'ct.csv')\n\n# Predict on all skills on the training data.\n# This returns a Pandas DataFrame.\npreds_df = model.predict(data_path = 'ct.csv')\n\n# Evaluate the RMSE of the model on the training data.\n# Note that the default evaluate metric is RMSE.\ntraining_rmse = model.evaluate(data = ct_df)\n\n# Evaluate the AUC of the model on the training data. The supported\n# metrics are AUC, RMSE and accuracy (they should be lowercased in\n# the argument!).\ntraining_auc = model.evaluate(data_path = 'ct.csv', metric = 'auc')\n\n# We can define a custom metric as well.\ndef mae(true_vals, pred_vals):\n \u0026quot;\u0026quot;\u0026quot; Calculates the mean absolute error. \u0026quot;\u0026quot;\u0026quot;\n return np.mean(np.abs(true_vals - pred_vals))\n\ntraining_mae = model.evaluate(data_path = 'ct.csv', metric = mae)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epyBKT\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003emodels\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eModel\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Initialize the model with an optional seed\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eModel\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eseed\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e42\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enum_fits\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Load the Cognitive Tutor data (not necessary, but shown\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# for the purposes of the tutorial that pyBKT accepts\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# DataFrames as well as file locations!).\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003ect_df\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epd\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eread_csv\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eencoding\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'latin'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Train a simple BKT model on all skills in the CT dataset\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Predict on all skills on the training data.\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# This returns a Pandas DataFrame.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003epreds_df\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003epredict\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Evaluate the RMSE of the model on the training data.\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# Note that the default evaluate metric is RMSE.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003etraining_rmse\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eevaluate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ect_df\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Evaluate the AUC of the model on the training data. The supported\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# metrics are AUC, RMSE and accuracy (they should be lowercased in\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# the argument!).\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003etraining_auc\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eevaluate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emetric\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'auc'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# We can define a custom metric as well.\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003edef\u003c/span\u003e \u003cspan class=\"pl-en\"\u003emae\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etrue_vals\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003epred_vals\u003c/span\u003e):\n \u003cspan class=\"pl-s\"\u003e\"\"\" Calculates the mean absolute error. \"\"\"\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003emean\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eabs\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etrue_vals\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epred_vals\u003c/span\u003e))\n\n\u003cspan class=\"pl-s1\"\u003etraining_mae\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eevaluate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emetric\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emae\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCrossvalidation\u003c/h2\u003e\u003ca id=\"user-content-crossvalidation\" class=\"anchor\" aria-label=\"Permalink: Crossvalidation\" href=\"#crossvalidation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCrossvalidation is offered as a blackbox function similar to a combination of fit and evaluate that accepts a particular number of folds, a seed, and a metric (either one of the 3 provided that are 'rmse', 'auc' or 'accuracy' or a custom Python function taking 2 arguments). Similar arguments for the model types, data path/data, and skill names are accepted as with the fit function.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"from pyBKT.models import Model\n\n# Initialize the model with an optional seed\nmodel = Model(seed = 42, num_fits = 1)\n\n# Crossvalidate with 5 folds on all skills in the CT dataset.\ncrossvalidated_errors = model.crossvalidate(data_path = 'ct.csv', folds = 5)\n\n# Crossvalidate on a particular set of skills with a given \n# seed, folds and metric.\ndef mae(true_vals, pred_vals):\n \u0026quot;\u0026quot;\u0026quot; Calculates the mean absolute error. \u0026quot;\u0026quot;\u0026quot;\n return np.mean(np.abs(true_vals - pred_vals))\n\n# Note that the skills argument accepts a REGEX pattern. In this case, this matches and \n# crossvalidates on all skills containing the word fraction.\ncrossvalidated_mae_errs = model.crossvalidate(data_path = 'ct.csv', skills = \u0026quot;.*fraction.*\u0026quot;,\n folds = 10, metric = mae)\n\n# Crossvalidate using multiple model variants.\ncrossvalidated_multigsf = model.crossvalidate(data_path = 'ct.csv', multigs = True, forgets = True)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epyBKT\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003emodels\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eModel\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Initialize the model with an optional seed\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eModel\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eseed\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e42\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enum_fits\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Crossvalidate with 5 folds on all skills in the CT dataset.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003ecrossvalidated_errors\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ecrossvalidate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003efolds\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Crossvalidate on a particular set of skills with a given \u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# seed, folds and metric.\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003edef\u003c/span\u003e \u003cspan class=\"pl-en\"\u003emae\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etrue_vals\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003epred_vals\u003c/span\u003e):\n \u003cspan class=\"pl-s\"\u003e\"\"\" Calculates the mean absolute error. \"\"\"\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003emean\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eabs\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etrue_vals\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epred_vals\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# Note that the skills argument accepts a REGEX pattern. In this case, this matches and \u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# crossvalidates on all skills containing the word fraction.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003ecrossvalidated_mae_errs\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ecrossvalidate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\".*fraction.*\"\u003c/span\u003e,\n \u003cspan class=\"pl-s1\"\u003efolds\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e10\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emetric\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emae\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Crossvalidate using multiple model variants.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003ecrossvalidated_multigsf\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ecrossvalidate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emultigs\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eforgets\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRoster\u003c/h2\u003e\u003ca id=\"user-content-roster\" class=\"anchor\" aria-label=\"Permalink: Roster\" href=\"#roster\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe model has been extended into the Roster to accomodate and simulate the learning environment for a cohort of students learning any combination of individual skills. The Roster feature has the efficient ability to track individuals' progress through the mastery and correctness probabilities outputted by BKT by storing only the current latent and observable state of the student. The following shows an example of Roster being used in practise:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"from pyBKT.models import *\nimport numpy as np\n\n# Create a backend pyBKT model and fit it on the CT data\nmodel = Model()\nmodel.fit(data_path = 'ct.csv')\n\n# Create a Roster with two students, Jeff and Bob, who are participating in the roster\n# for one skill (Calculate Unit Rate) using the pyBKT model above.\nroster = Roster(students = ['Jeff', 'Bob'], skills = 'Calculate unit rate', model = model)\n\n# Initial mastery state (prior) for Jeff, should be unmastered with low probability of mastery\n# get_state_type returns whether a student has mastered the skill or not\n# get_mastery_prob returns the probability a student has mastered the skill\nprint(\u0026quot;Jeff's mastery (t = 0):\u0026quot;, roster.get_state_type('Calculate unit rate', 'Jeff'))\nprint(\u0026quot;Jeff's probability of mastery (t = 0):\u0026quot;, roster.get_mastery_prob('Calculate unit rate', 'Jeff'))\n\n# We can update Jeff's state by adding one or more responses to a particular skill. In this case,\n# we observed a correct response for the one skill in the roster.\njeff_new_state = roster.update_state('Calculate unit rate', 'Jeff', 1)\n\n# Check the updated mastery state and probability.\nprint(\u0026quot;Jeff's mastery (t = 1):\u0026quot;, roster.get_state_type('Calculate unit rate', 'Jeff'))\nprint(\u0026quot;Jeff's probability of mastery (t = 1):\u0026quot;, roster.get_mastery_prob('Calculate unit rate', 'Jeff'))\n\n# We can update his state with multiple correct responses (ten of them).\nroster.update_state('Calculate unit rate', 'Jeff', np.ones(10))\n\n# After 10 consecutive correct responses, he should have mastered the skill.\nprint(\u0026quot;Jeff's mastery (t = 11):\u0026quot;, roster.get_state_type('Calculate unit rate', 'Jeff'))\nprint(\u0026quot;Jeff's probability of mastery (t = 11):\u0026quot;, roster.get_mastery_prob('Calculate unit rate', 'Jeff'))\n\n# Programmatically check whether he has mastered the skill\nif roster.get_state_type('Calculate unit rate', 'Jeff') == StateType.MASTERED:\n print(\u0026quot;Jeff has mastered the skill!\u0026quot;)\n \n# We can update Bob's state with two correct responses.\nroster.update_state('Calculate unit rate', 'Bob', np.ones(2))\n\n# He should remain unmastered.\nprint(\u0026quot;Bob's mastery (t = 2):\u0026quot;, roster.get_state_type('Calculate unit rate', 'Bob'))\nprint(\u0026quot;Bob's probability of mastery (t = 2):\u0026quot;, roster.get_mastery_prob('Calculate unit rate', 'Bob'))\n\n# We can print aggregate statistics for mastery and correctness.\nprint(\u0026quot;Both students' probabilites of correctness:\u0026quot;, roster.get_correct_probs('Calculate unit rate'))\nprint(\u0026quot;Both students' probabilites of mastery:\u0026quot;, roster.get_mastery_probs('Calculate unit rate'))\n\n# Add a new student, Sarah.\nroster.add_student('Calculate unit rate', 'Sarah')\n\n# Update Sarah's state with a sequence of correct and incorrect responses.\nsarah_new_state = roster.update_state('Calculate unit rate', 'Sarah', np.array([1, 0, 1, 0, 1, 1, 1]))\n\n# Print Sarah's correctness and mastery probability.\nprint(\u0026quot;Sarah's correctness probability:\u0026quot;, sarah_new_state.get_correct_prob()\nprint(\u0026quot;Sarah's mastery probability:\u0026quot;, sarah_new_state.get_mastery_prob())\n\n# Delete Bob from the roster.\nroster.remove_student('Calculate unit rate', 'Bob')\n\n# Reset student's state (i.e. latent and observable).\nroster.reset_state('Calculate unit rate', 'Jeff')\n\n# Jeff should be back to the initial prior as the mastery probability and should be unmastered.\nprint(\u0026quot;Jeff's mastery (t' = 0):\u0026quot;, roster.get_state_type('Calculate unit rate', 'Jeff'))\nprint(\u0026quot;Jeff's probability of mastery (t' = 0):\u0026quot;, roster.get_mastery_prob('Calculate unit rate', 'Jeff'))\n\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epyBKT\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003emodels\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e*\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Create a backend pyBKT model and fit it on the CT data\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eModel\u003c/span\u003e()\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Create a Roster with two students, Jeff and Bob, who are participating in the roster\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# for one skill (Calculate Unit Rate) using the pyBKT model above.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eRoster\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estudents\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e [\u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Bob'\u003c/span\u003e], \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Initial mastery state (prior) for Jeff, should be unmastered with low probability of mastery\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# get_state_type returns whether a student has mastered the skill or not\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# get_mastery_prob returns the probability a student has mastered the skill\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's mastery (t = 0):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's probability of mastery (t = 0):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# We can update Jeff's state by adding one or more responses to a particular skill. In this case,\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# we observed a correct response for the one skill in the roster.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003ejeff_new_state\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eupdate_state\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Check the updated mastery state and probability.\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's mastery (t = 1):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's probability of mastery (t = 1):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# We can update his state with multiple correct responses (ten of them).\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eupdate_state\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eones\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e10\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# After 10 consecutive correct responses, he should have mastered the skill.\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's mastery (t = 11):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's probability of mastery (t = 11):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# Programmatically check whether he has mastered the skill\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003eif\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003e==\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eStateType\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eMASTERED\u003c/span\u003e:\n \u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff has mastered the skill!\"\u003c/span\u003e)\n \n\u003cspan class=\"pl-c\"\u003e# We can update Bob's state with two correct responses.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eupdate_state\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Bob'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eones\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# He should remain unmastered.\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Bob's mastery (t = 2):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Bob'\u003c/span\u003e))\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Bob's probability of mastery (t = 2):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Bob'\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# We can print aggregate statistics for mastery and correctness.\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Both students' probabilites of correctness:\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_correct_probs\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e))\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Both students' probabilites of mastery:\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_probs\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e))\n\n\u003cspan class=\"pl-c\"\u003e# Add a new student, Sarah.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eadd_student\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Sarah'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Update Sarah's state with a sequence of correct and incorrect responses.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003esarah_new_state\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eupdate_state\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Sarah'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003earray\u003c/span\u003e([\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e]))\n\n\u003cspan class=\"pl-c\"\u003e# Print Sarah's correctness and mastery probability.\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Sarah's correctness probability:\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003esarah_new_state\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_correct_prob\u003c/span\u003e()\n\u003cspan class=\"pl-s1\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Sarah's mastery probability:\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003esarah_new_state\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e())\n\n\u003cspan class=\"pl-c\"\u003e# Delete Bob from the roster.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eremove_student\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Bob'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Reset student's state (i.e. latent and observable).\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ereset_state\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e)\n\n\u003cspan class=\"pl-c\"\u003e# Jeff should be back to the initial prior as the mastery probability and should be unmastered.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's mastery (t' = 0):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_state_type\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\n\u003cspan class=\"pl-s1\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Jeff's probability of mastery (t' = 0):\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eroster\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eget_mastery_prob\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'Calculate unit rate'\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'Jeff'\u003c/span\u003e))\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eParameter Fixing\u003c/h2\u003e\u003ca id=\"user-content-parameter-fixing\" class=\"anchor\" aria-label=\"Permalink: Parameter Fixing\" href=\"#parameter-fixing\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAnother advanced feature supported by pyBKT is parameter fixing, where we can fix one or more parameters and train the model conditioned on those fixed parameters. This can be useful if you already know the ground truth value of some parameters beforehand, or to avoid degenerate model creation by fixing parameters at reasonable values. To specify which parameters and values we want fixed for any skill, we can pass in a dictionary to model.coef_, and then specify fixed=True in the model.fit call:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"from pyBKT.models import *\nimport numpy as np\nmodel = Model()\n\n# Fixes the prior rate and learn rate to 0.1 for the Plot imperfect radical skill, and trains the model given those fixed parameters.\nmodel.coef_ = {'Plot imperfect radical': {'prior': 0.1, 'learns': np.array([0.1])}}\nmodel.fit(data_path = 'ct.csv', skills='Plot imperfect radical', fixed=True)\nmodel.params()\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epyBKT\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003emodels\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e*\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eModel\u003c/span\u003e()\n\n\u003cspan class=\"pl-c\"\u003e# Fixes the prior rate and learn rate to 0.1 for the Plot imperfect radical skill, and trains the model given those fixed parameters.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ecoef_\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e {\u003cspan class=\"pl-s\"\u003e'Plot imperfect radical'\u003c/span\u003e: {\u003cspan class=\"pl-s\"\u003e'prior'\u003c/span\u003e: \u003cspan class=\"pl-c1\"\u003e0.1\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'learns'\u003c/span\u003e: \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003earray\u003c/span\u003e([\u003cspan class=\"pl-c1\"\u003e0.1\u003c/span\u003e])}}\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-s\"\u003e'Plot imperfect radical'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003efixed\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e)\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eparams\u003c/span\u003e()\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWithin the model.coef_ dictionary, the 'prior' parameter takes a scalar, while 'learns', 'forgets', 'guesses', and 'slips' takes an np.array, in order to provide support for parameter fixing in model extensions with multiple learn or guess classes. An example of such is shown below.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"# The Plot pi skill has 10 different guess/slip classes. This is how you would fix those slip classes to 0, 0.1, ..., 0.9 and train the model conditioned on those slip values.\nmodel.coef_ = {'Plot pi': {'slips': np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])}}\nmodel.fit(data_path = 'ct.csv', skills='Plot pi', multigs=True, fixed=True)\nmodel.params()\"\u003e\u003cpre\u003e\u003cspan class=\"pl-c\"\u003e# The Plot pi skill has 10 different guess/slip classes. This is how you would fix those slip classes to 0, 0.1, ..., 0.9 and train the model conditioned on those slip values.\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003ecoef_\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e {\u003cspan class=\"pl-s\"\u003e'Plot pi'\u003c/span\u003e: {\u003cspan class=\"pl-s\"\u003e'slips'\u003c/span\u003e: \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003earray\u003c/span\u003e([\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.5\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.6\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.7\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.8\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0.9\u003c/span\u003e])}}\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003efit\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edata_path\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e'ct.csv'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eskills\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-s\"\u003e'Plot pi'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003emultigs\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003efixed\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eTrue\u003c/span\u003e)\n\u003cspan class=\"pl-s1\"\u003emodel\u003c/span\u003e.\u003cspan class=\"pl-c1\"\u003eparams\u003c/span\u003e()\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eExtended Features\u003c/h2\u003e\u003ca id=\"user-content-extended-features\" class=\"anchor\" aria-label=\"Permalink: Extended Features\" href=\"#extended-features\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExtended features include model parameter initialization by setting model.coef_, providing a configuration dictionary, setting model default columns, and more. For more information about these features, take a look at the Colab notebook provided at the top of the README.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInternal Data Format\u003c/h1\u003e\u003ca id=\"user-content-internal-data-format\" class=\"anchor\" aria-label=\"Permalink: Internal Data Format\" href=\"#internal-data-format\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003cem\u003epyBKT\u003c/em\u003e models student mastery of a skills as they progress through series of learning resources and checks for understanding. Mastery is modelled as a latent variable has two states - \"knowing\" and \"not knowing\". At each checkpoint, students may be given a learning resource (i.e. watch a video) and/or question(s) to check for understanding. The model finds the probability of learning, forgetting, slipping and guessing that maximizes the likelihood of observed student responses to questions.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo run the pyBKT model, define the following variables:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003enum_subparts\u003c/code\u003e: The number of unique questions used to check understanding. Each subpart has a unique set of emission probabilities.\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003enum_resources\u003c/code\u003e: The number of unique learning resources available to students.\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003enum_fit_initialization\u003c/code\u003e: The number of iterations in the EM step.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eNext, create an input object \u003ccode\u003eData\u003c/code\u003e, containing the following attributes:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003edata\u003c/code\u003e: a matrix containing sequential checkpoints for all students, with their responses. Each row represents a different subpart, and each column a checkpoint for a student. There are three potential values: {0 = no response or no question asked, 1 = wrong response, 2 = correct response}. If at a checkpoint, a resource was given but no question asked, the associated column would have \u003ccode\u003e0\u003c/code\u003e values in all rows. For example, to set up data containing 5 subparts given to two students over 2-3 checkpoints, the matrix would look as follows:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" | 0 0 0 0 2 |\n | 0 1 0 0 0 |\n | 0 0 0 0 0 |\n | 0 0 0 0 0 |\n | 0 0 2 0 0 | \"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e | 0 0 0 0 2 |\n | 0 1 0 0 0 |\n | 0 0 0 0 0 |\n | 0 0 0 0 0 |\n | 0 0 2 0 0 | \n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn the above example, the first student starts out with just a learning resource, and no checks for understanding. In subsequent checkpoints, this student also responds to subpart 2 and 5, and gets the first wrong and the second correct.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003estarts\u003c/code\u003e: defines each student's starting column on the \u003ccode\u003edata\u003c/code\u003e matrix. For the above matrix, \u003ccode\u003estarts\u003c/code\u003e would be defined as:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" | 1 4 |\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e | 1 4 |\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003elengths\u003c/code\u003e: defines the number of check point for each student. For the above matrix, \u003ccode\u003elengths\u003c/code\u003e would be defined as:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" | 3 2 |\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e | 3 2 |\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eresources\u003c/code\u003e: defines the sequential id of the resources at each checkpoint. Each position in the vector corresponds to the column in the \u003ccode\u003edata\u003c/code\u003e matrix. For the above matrix, the learning \u003ccode\u003eresources\u003c/code\u003e at each checkpoint would be structured as:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" | 1 2 1 1 3 |\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e | 1 2 1 1 3 |\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003estateseqs\u003c/code\u003e: this attribute is the true knowledge state for above data and should be left undefined before running the \u003ccode\u003epyBKT\u003c/code\u003e model.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe output of the model can will be stored in a \u003ccode\u003efitmodel\u003c/code\u003e object, containing the following probabilities as attributes:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eAs\u003c/code\u003e: the transition probability between the \"knowing\" and \"not knowing\" state. Includes both the \u003ccode\u003elearns\u003c/code\u003e and \u003ccode\u003eforgets\u003c/code\u003e probabilities, and their inverse. \u003ccode\u003eAs\u003c/code\u003e creates a separate transition probability for each resource.\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003elearns\u003c/code\u003e: the probability of transitioning to the \"knowing\" state given \"not known\".\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eforgets\u003c/code\u003e: the probability of transitioning to the \"not knowing\" state given \"known\".\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eprior\u003c/code\u003e: the prior probability of \"knowing\".\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe \u003ccode\u003efitmodel\u003c/code\u003e also includes the following emission probabilities:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eguesses\u003c/code\u003e: the probability of guessing correctly, given \"not knowing\" state.\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eslips\u003c/code\u003e: the probability of picking incorrect answer, given \"knowing\" state.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCitation\u003c/h2\u003e\u003ca id=\"user-content-citation\" class=\"anchor\" aria-label=\"Permalink: Citation\" href=\"#citation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo credit this library, please cite our paper published in the Educaitonal Data Mining Conference:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBadrinath, A., Wang, F., Pardos, Z.A. (2021) pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models. In S. Hsiao, \u0026amp; S. Sahebi (Eds.) \u003cem\u003eProceedings of the 14th International Conference on Educational Data Mining\u003c/em\u003e (EDM). Pages 468-474.\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"@inproceedings{badrinath2021pybkt,\n title={pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models},\n author={Badrinath, Anirudhan and Wang, Frederic and Pardos, Zachary},\n booktitle={Proceedings of the 14th International Conference on Educational Data Mining},\n pages={468--474},\n year={2021}\n}\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e@inproceedings{badrinath2021pybkt,\n title={pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models},\n author={Badrinath, Anirudhan and Wang, Frederic and Pardos, Zachary},\n booktitle={Proceedings of the 14th International Conference on Educational Data Mining},\n pages={468--474},\n year={2021}\n}\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTODOs\u003c/h2\u003e\u003ca id=\"user-content-todos\" class=\"anchor\" aria-label=\"Permalink: TODOs\" href=\"#todos\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eExporting compiled binaries on PyPi\u003c/li\u003e\n\u003cli\u003eAdditional model variants\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"pyBKT","anchor":"pybkt","htmlText":"pyBKT"},{"level":2,"text":"Requirements","anchor":"requirements","htmlText":"Requirements"},{"level":2,"text":"Supported model variants","anchor":"supported-model-variants","htmlText":"Supported model variants"},{"level":1,"text":"Installation and setup","anchor":"installation-and-setup","htmlText":"Installation and setup"},{"level":2,"text":"Installing Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)","anchor":"installing-dependencies-for-fast-c-inferencing-optional---for-os-x-and-linux","htmlText":"Installing Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)"},{"level":3,"text":"Linux","anchor":"linux","htmlText":"Linux"},{"level":3,"text":"Mac","anchor":"mac","htmlText":"Mac"},{"level":2,"text":"Installing pyBKT","anchor":"installing-pybkt","htmlText":"Installing pyBKT"},{"level":1,"text":"Preparing Data and Running Model","anchor":"preparing-data-and-running-model","htmlText":"Preparing Data and Running Model"},{"level":2,"text":"Input and Output Data","anchor":"input-and-output-data","htmlText":"Input and Output Data"},{"level":2,"text":"Creating and Training Models","anchor":"creating-and-training-models","htmlText":"Creating and Training Models"},{"level":2,"text":"Model Prediction and Evaluation","anchor":"model-prediction-and-evaluation","htmlText":"Model Prediction and Evaluation"},{"level":2,"text":"Crossvalidation","anchor":"crossvalidation","htmlText":"Crossvalidation"},{"level":2,"text":"Roster","anchor":"roster","htmlText":"Roster"},{"level":2,"text":"Parameter Fixing","anchor":"parameter-fixing","htmlText":"Parameter Fixing"},{"level":2,"text":"Extended Features","anchor":"extended-features","htmlText":"Extended Features"},{"level":1,"text":"Internal Data Format","anchor":"internal-data-format","htmlText":"Internal Data Format"},{"level":2,"text":"Citation","anchor":"citation","htmlText":"Citation"},{"level":2,"text":"TODOs","anchor":"todos","htmlText":"TODOs"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2FCAHLR%2FpyBKT"}},{"displayName":"LICENSE","repoName":"pyBKT","refName":"master","path":"LICENSE","preferredFileType":"license","tabName":"MIT","richText":null,"loaded":false,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":null,"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2FCAHLR%2FpyBKT"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-7d7eb7c71814.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-708ec8ade250.js","githubDevUrl":null,"enabled_features":{"copilot_workspace":null,"code_nav_ui_events":false,"react_blob_overlay":false,"accessible_code_button":true,"github_models_repo_integration":false}}}}</script>
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aria-describedby=":Rr9ab:-loading-announcement" id=":Rr9ab:"><svg aria-hidden="true" focusable="false" class="octicon octicon-list-unordered" viewBox="0 0 16 16" width="16" height="16" fill="currentColor" display="inline-block" overflow="visible" style="vertical-align:text-bottom"><path d="M5.75 2.5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5ZM2 14a1 1 0 1 1 0-2 1 1 0 0 1 0 2Zm1-6a1 1 0 1 1-2 0 1 1 0 0 1 2 0ZM2 4a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path></svg></button></div><div class="Box-sc-g0xbh4-0 QkQOb js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">pyBKT</h1><a id="user-content-pybkt" class="anchor" aria-label="Permalink: pyBKT" href="#pybkt"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Python implementation of the Bayesian Knowledge Tracing algorithm and variants, estimating student cognitive mastery from problem solving sequences.</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" pip install pyBKT"><pre class="notranslate"><code> pip install pyBKT
</code></pre></div>
<p dir="auto">Based on the work of Zachary A. Pardos (<a href="mailto:[email protected]">[email protected]</a>) and Matthew J. Johnson (<a href="mailto:[email protected]">[email protected]</a>) @ <a href="https://github.com/CAHLR/xBKT">https://github.com/CAHLR/xBKT</a>. All-platform python adaptation and optimizations by Anirudhan Badrinath (<a href="mailto:[email protected]">[email protected]</a>). Data helpers and other utility functions written by Frederic Wang (<a href="mailto:[email protected]">[email protected]</a>). Original Python and boost adaptation of xBKT by Cristian Garay (<a href="mailto:[email protected]">[email protected]</a>). For implementation details, analysis of runtime and data requirements, and model variant replication testing, refer to:</p>
<p dir="auto">Badrinath, A., Wang, F., Pardos, Z.A. (2021) <a href="https://educationaldatamining.org/EDM2021/virtual/static/pdf/EDM21_paper_237.pdf" rel="nofollow">pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models</a>. In S. Hsiao, & S. Sahebi (Eds.) <em>Proceedings of the 14th International Conference on Educational Data Mining</em> (EDM). Pages 468-474.</p>
<p dir="auto">Bulut, O., Shin, J., Yildirim-Erbasli, S. N., Gorgun, G., & Pardos, Z. A. (2023). <a href="https://www.mdpi.com/2624-8611/5/3/50" rel="nofollow">An introduction to Bayesian knowledge tracing with pyBKT</a>. <em>Psych</em>, 5(3), 770-786.</p>
<p dir="auto">Examples from the paper can be found in <a href="https://github.com/CAHLR/pyBKT-examples/" title="pyBKT examples">pyBKT-examples</a> repo.</p>
<p dir="auto"><a href="https://colab.research.google.com/drive/13abu919edUXbvPV3qeGPpvwnFBExU7Vd" title="pyBKT quick start in Colab" rel="nofollow">pyBKT Quick Start Tutorial</a></p>
<p dir="auto"><a href="https://colab.research.google.com/drive/1Kg6AvXKdSZXoqzSZ5BRHuewyHRMvrZs1" title="pyBKT quick start in Colab" rel="nofollow">pyBKT Tutorial from LAK Workshop in Google Colab Notebook</a></p>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Requirements</h2><a id="user-content-requirements" class="anchor" aria-label="Permalink: Requirements" href="#requirements"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Python >= 3.5</p>
<p dir="auto">Supported OS: All platforms! (Yes, Windows too)</p>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Supported model variants</h2><a id="user-content-supported-model-variants" class="anchor" aria-label="Permalink: Supported model variants" href="#supported-model-variants"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">pyBKT can be used to define and fit many BKT variants, including these from the literature:</p>
<ul dir="auto">
<li>Individual student priors, learn rate, guess, and slip [1,2]</li>
<li>Individual item guess and slip [3,4,5]</li>
<li>Individual item or resource learn rate [4,5]</li>
</ul>
<ol dir="auto">
<li>
<p dir="auto">Pardos, Z. A., Heffernan, N. T. (2010) Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing. In P. De Bra, A. Kobsa, D. Chin (Eds.) <em>Proceedings of the 18th International Conference on User Modeling, Adaptation and Personalization</em> (UMAP). Big Island of Hawaii. Pages. Springer. Pages 255-266. <a href="https://doi.org/10.1007/978-3-642-13470-8_24" rel="nofollow">[doi]</a></p>
</li>
<li>
<p dir="auto">Pardos, Z. A., Heffernan, N. T. (2010) Using HMMs and bagged decision trees to leverage rich features of user and skill from an intelligent tutoring system dataset. In J. Stamper & A. Niculescu-Mizil (Eds.) <em>Proceedings of the KDD Cup Workshop at the 16th ACM Conference on Knowledge Discovery and Data Mining</em> (SIGKDD). Washington, D.C. ACM. Pages 24-35. <a href="https://pslcdatashop.web.cmu.edu/KDDCup/workshop/papers/pardos_heffernan_KDD_Cup_2010_article.pdf" rel="nofollow">[kdd cup]</a></p>
</li>
<li>
<p dir="auto">Pardos, Z. & Heffernan, N. (2011) KT-IDEM: Introducing Item Difficulty to the Knowledge Tracing Model. In Konstant et al. (eds.) <em>Proceedings of the 20th International Conference on User Modeling, Adaptation and Personalization</em> (UMAP). Girona, Spain. Springer. Pages 243-254. <a href="https://doi.org/10.1007/978-3-642-22362-4_21" rel="nofollow">[doi]</a></p>
</li>
<li>
<p dir="auto">Pardos, Z. A., Bergner, Y., Seaton, D., Pritchard, D.E. (2013) Adapting Bayesian Knowledge Tracing to a Massive Open Online College Course in edX. In S.K. D’Mello, R.A. Calvo, & A. Olney (Eds.) <em>Proceedings of the 6th International Conference on Educational Data Mining</em> (EDM). Memphis, TN. Pages 137-144. <a href="http://educationaldatamining.org/EDM2013/proceedings/paper_20.pdf" rel="nofollow">[edm]</a></p>
</li>
<li>
<p dir="auto">Xu, Y., Johnson, M. J., Pardos, Z. A. (2015) Scaling cognitive modeling to massive open environments. In <em>Proceedings of the Workshop on Machine Learning for Education at the 32nd International Conference on Machine Learning</em> (ICML). Lille, France. <a href="http://ml4ed.cc/attachments/XuY.pdf" rel="nofollow">[icml ml4ed]</a></p>
</li>
</ol>
<div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Installation and setup</h1><a id="user-content-installation-and-setup" class="anchor" aria-label="Permalink: Installation and setup" href="#installation-and-setup"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">This is intended as a quick overview of steps to install and setup and to run pyBKT locally.</p>
<p dir="auto">We offer both a pure Python port and a Python/C++ extension version of pyBKT for the sake of accessibility and ease of use on any platform. Note that pip, by default, will install the C++/Python version unless the required libraries are not found or there is an error during installation. In the case of such issues, it will revert to the pure Python implementation.</p>
<p dir="auto">The former pure Python versions does not fit models or scale as quickly or efficiently as the latter (due to nested for loops needed for DP). Here are a few speed comparisons - both on the same machine - that may be useful in deciding which version is more appropriate given the usage (e.g. model fitting is far more demanding than prediction).</p>
<markdown-accessiblity-table><table>
<thead>
<tr>
<th align="center">Test Description</th>
<th align="center">pyBKT (Python)</th>
<th align="right">pyBKT (C++)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">synthetic data, model fit (500 students)</td>
<td align="center">~1m55s</td>
<td align="right">~1.5s</td>
</tr>
<tr>
<td align="center">synthetic data, model fit (5000 students)</td>
<td align="center">~1h30m</td>
<td align="right">~45s</td>
</tr>
<tr>
<td align="center">cross validated cognitive tutor data</td>
<td align="center">~4m10s</td>
<td align="right">~3s</td>
</tr>
<tr>
<td align="center">synthetic data, predict onestep (500 students)</td>
<td align="center">~2s</td>
<td align="right">~0.8s</td>
</tr>
<tr>
<td align="center">synthetic data, predict onestep (5000 students)</td>
<td align="center">~2m15s</td>
<td align="right">~35s</td>
</tr>
</tbody>
</table></markdown-accessiblity-table>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Installing Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)</h2><a id="user-content-installing-dependencies-for-fast-c-inferencing-optional---for-os-x-and-linux" class="anchor" aria-label="Permalink: Installing Dependencies for Fast C++ Inferencing (Optional - for OS X and Linux)" href="#installing-dependencies-for-fast-c-inferencing-optional---for-os-x-and-linux"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Note: this section is not applicable for Windows as running the Python/C++ version is cumbersome and untested. For Windows, we only offer the slower, pure Python version of pyBKT (it will be installed automatically).</p>
<div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Linux</h3><a id="user-content-linux" class="anchor" aria-label="Permalink: Linux" href="#linux"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">If you have a C++ compiler already installed, pip will install pyBKT with fast C++ inferencing. C++ compilers are already installed on nearly all Linux distributions. If it is not installed on your machine, type <code>sudo apt install gcc g++</code> if using Debian based distributions. Otherwise, whichever package manager is appropriately suited to your distribution (<code>dnf</code>, <code>pacman</code>, etc.). Without a compiler, pip will install pyBKT without C++ speed optimizations.</p>
<div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Mac</h3><a id="user-content-mac" class="anchor" aria-label="Permalink: Mac" href="#mac"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">The latest version of Python is necessary for OS X. If homebrew is installed, run the following commands to download the necessary dependencies:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" brew install libomp"><pre class="notranslate"><code> brew install libomp
</code></pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Installing pyBKT</h2><a id="user-content-installing-pybkt" class="anchor" aria-label="Permalink: Installing pyBKT" href="#installing-pybkt"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">You can simply run:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" pip install pyBKT"><pre class="notranslate"><code> pip install pyBKT
</code></pre></div>
<p dir="auto">Alternatively, if <code>pip</code> poses some problems, you can clone the repository as such and then run the <code>setup.py</code> script manually.</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" git clone https://github.com/CAHLR/pyBKT.git
cd pyBKT
python3 setup.py install"><pre class="notranslate"><code> git clone https://github.com/CAHLR/pyBKT.git
cd pyBKT
python3 setup.py install
</code></pre></div>
<div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Preparing Data and Running Model</h1><a id="user-content-preparing-data-and-running-model" class="anchor" aria-label="Permalink: Preparing Data and Running Model" href="#preparing-data-and-running-model"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">The following serves as a mini-tutorial for how to get started with pyBKT. There is more information available at the Colab notebook listed at the top of the README.</p>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Input and Output Data</h2><a id="user-content-input-and-output-data" class="anchor" aria-label="Permalink: Input and Output Data" href="#input-and-output-data"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">The accepted input formats are Pandas DataFrames and data files of type csv (comma separated) or tsv (tab separated). pyBKT will automatically infer which delimiter to use in the case that it is passed a data file. Since column names mapping meaning to each field in the data (i.e. skill name, correct/incorrect) vary per data source, you may need to specify a mapping from your data file's column names to pyBKT's expected column names. In many cases with Cognitive Tutor and Assistments datasets, pyBKT will be able to automatically infer column name mappings, but in the case that it is unable to, it will raise an exception. Note that the correctness is given by -1 (no response), 0 (incorrect), or 1 (correct).</p>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Creating and Training Models</h2><a id="user-content-creating-and-training-models" class="anchor" aria-label="Permalink: Creating and Training Models" href="#creating-and-training-models"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">The process of creating and training models in pyBKT resemble that of SciKit Learn. pyBKT provides easy methods of fetching online datasets and to fit on a combination or all skills available in any particular dataset.</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="from pyBKT.models import Model
# Initialize the model with an optional seed
model = Model(seed = 42, num_fits = 1)
# Fetch Assistments and CognitiveTutor data (optional - if you have your own dataset, that's fine too!)
model.fetch_dataset('https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/as.csv', '.')
model.fetch_dataset('https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/ct.csv', '.')
# Train a simple BKT model on all skills in the CT dataset
model.fit(data_path = 'ct.csv')
# Train a simple BKT model on one skill in the CT dataset
# Note that calling fit deletes any previous trained BKT model!
model.fit(data_path = 'ct.csv', skills = "Plot imperfect radical")
# Train a simple BKT model on multiple skills in the CT dataset
model.fit(data_path = 'ct.csv', skills = ["Plot imperfect radical",
"Plot pi"])
# Train a multiguess and slip BKT model on multiple skills in the
# CT dataset. Note: if you are not using CognitiveTutor or Assistments
# data, you may need to provide a column mapping for the guess/slip
# classes to use (i.e. if the column name is gsclasses, you would
# specify multigs = 'gsclasses' or specify a defaults dictionary
# defaults = {'multigs': 'gsclasses'}).
model.fit(data_path = 'ct.csv', skills = ["Plot imperfect radical",
"Plot pi"],
multigs = True)
# We can combine multiple model variants.
model.fit(data_path = 'ct.csv', skills = ["Plot imperfect radical",
"Plot pi"],
multigs = True, forgets = True,
multilearn = True)
# We can use a different column to specify the different learn and
# forget classes. In this case, we use student ID.
model.fit(data_path = 'ct.csv', skills = ["Plot imperfect radical",
"Plot pi"],
multigs = True, forgets = True,
multilearn = 'Anon Student Id')
# View the trained parameters!
print(model.params())"><pre><span class="pl-k">from</span> <span class="pl-s1">pyBKT</span>.<span class="pl-s1">models</span> <span class="pl-k">import</span> <span class="pl-v">Model</span>
<span class="pl-c"># Initialize the model with an optional seed</span>
<span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-en">Model</span>(<span class="pl-s1">seed</span> <span class="pl-c1">=</span> <span class="pl-c1">42</span>, <span class="pl-s1">num_fits</span> <span class="pl-c1">=</span> <span class="pl-c1">1</span>)
<span class="pl-c"># Fetch Assistments and CognitiveTutor data (optional - if you have your own dataset, that's fine too!)</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fetch_dataset</span>(<span class="pl-s">'https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/as.csv'</span>, <span class="pl-s">'.'</span>)
<span class="pl-s1">model</span>.<span class="pl-c1">fetch_dataset</span>(<span class="pl-s">'https://raw.githubusercontent.com/CAHLR/pyBKT-examples/master/data/ct.csv'</span>, <span class="pl-s">'.'</span>)
<span class="pl-c"># Train a simple BKT model on all skills in the CT dataset</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>)
<span class="pl-c"># Train a simple BKT model on one skill in the CT dataset</span>
<span class="pl-c"># Note that calling fit deletes any previous trained BKT model!</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> <span class="pl-s">"Plot imperfect radical"</span>)
<span class="pl-c"># Train a simple BKT model on multiple skills in the CT dataset</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> [<span class="pl-s">"Plot imperfect radical"</span>,
<span class="pl-s">"Plot pi"</span>])
<span class="pl-c"># Train a multiguess and slip BKT model on multiple skills in the</span>
<span class="pl-c"># CT dataset. Note: if you are not using CognitiveTutor or Assistments</span>
<span class="pl-c"># data, you may need to provide a column mapping for the guess/slip</span>
<span class="pl-c"># classes to use (i.e. if the column name is gsclasses, you would</span>
<span class="pl-c"># specify multigs = 'gsclasses' or specify a defaults dictionary</span>
<span class="pl-c"># defaults = {'multigs': 'gsclasses'}).</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> [<span class="pl-s">"Plot imperfect radical"</span>,
<span class="pl-s">"Plot pi"</span>],
<span class="pl-s1">multigs</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>)
<span class="pl-c"># We can combine multiple model variants.</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> [<span class="pl-s">"Plot imperfect radical"</span>,
<span class="pl-s">"Plot pi"</span>],
<span class="pl-s1">multigs</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>, <span class="pl-s1">forgets</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>,
<span class="pl-s1">multilearn</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>)
<span class="pl-c"># We can use a different column to specify the different learn and </span>
<span class="pl-c"># forget classes. In this case, we use student ID.</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> [<span class="pl-s">"Plot imperfect radical"</span>,
<span class="pl-s">"Plot pi"</span>],
<span class="pl-s1">multigs</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>, <span class="pl-s1">forgets</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>,
<span class="pl-s1">multilearn</span> <span class="pl-c1">=</span> <span class="pl-s">'Anon Student Id'</span>)
<span class="pl-c"># View the trained parameters!</span>
<span class="pl-en">print</span>(<span class="pl-s1">model</span>.<span class="pl-c1">params</span>())</pre></div>
<p dir="auto">Note that if we train on a dataset that has unfamiliar columns to pyBKT, you will be required to specify a mapping of column names in that dataset to expected pyBKT columns. This is referred to as the model defaults (i.e. it specifies the default column names to lookup in the dataset). An example usage is provided below for an unknown dataset which has column names "row", "skill_t", "answer", and "gs_classes".</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="# Load unfamiliar dataset.
df = pd.read_csv('mystery.csv')
# For other non-Assistments/CogTutor style datasets, we will need to specify the
# columns corresponding to each required column (i.e. the user ID, correct/incorrect).
# For that, we use a defaults dictionary.
# In this case, the order ID that pyBKT expects is specified by the column row in the
# dataset, the skill_name is specified by a column skill_t and the correctness is specified
# by the answer column in the dataset.
defaults = {'order_id': 'row', 'skill_name': 'skill_t', 'correct': 'answer'}
# This defaults dictionary contains columns specifying what columns correspond
# to the desired guess/slip classes, etc. In this case, our desired column for
# the guess/slip classes is a column named gs_classes.
defaults['multigs'] = 'gs_classes'
# Fit using the defaults (column mappings) specified in the dictionary.
model.fit(data = df, defaults = defaults)
# Predict/evaluate/etc.
training_acc = model.evaluate(data = df, metric = 'accuracy')"><pre><span class="pl-c"># Load unfamiliar dataset.</span>
<span class="pl-s1">df</span> <span class="pl-c1">=</span> <span class="pl-s1">pd</span>.<span class="pl-c1">read_csv</span>(<span class="pl-s">'mystery.csv'</span>)
<span class="pl-c"># For other non-Assistments/CogTutor style datasets, we will need to specify the</span>
<span class="pl-c"># columns corresponding to each required column (i.e. the user ID, correct/incorrect).</span>
<span class="pl-c"># For that, we use a defaults dictionary.</span>
<span class="pl-c"># In this case, the order ID that pyBKT expects is specified by the column row in the</span>
<span class="pl-c"># dataset, the skill_name is specified by a column skill_t and the correctness is specified</span>
<span class="pl-c"># by the answer column in the dataset.</span>
<span class="pl-s1">defaults</span> <span class="pl-c1">=</span> {<span class="pl-s">'order_id'</span>: <span class="pl-s">'row'</span>, <span class="pl-s">'skill_name'</span>: <span class="pl-s">'skill_t'</span>, <span class="pl-s">'correct'</span>: <span class="pl-s">'answer'</span>}
<span class="pl-c"># This defaults dictionary contains columns specifying what columns correspond</span>
<span class="pl-c"># to the desired guess/slip classes, etc. In this case, our desired column for</span>
<span class="pl-c"># the guess/slip classes is a column named gs_classes.</span>
<span class="pl-s1">defaults</span>[<span class="pl-s">'multigs'</span>] <span class="pl-c1">=</span> <span class="pl-s">'gs_classes'</span>
<span class="pl-c"># Fit using the defaults (column mappings) specified in the dictionary.</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data</span> <span class="pl-c1">=</span> <span class="pl-s1">df</span>, <span class="pl-s1">defaults</span> <span class="pl-c1">=</span> <span class="pl-s1">defaults</span>)
<span class="pl-c"># Predict/evaluate/etc.</span>
<span class="pl-s1">training_acc</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">evaluate</span>(<span class="pl-s1">data</span> <span class="pl-c1">=</span> <span class="pl-s1">df</span>, <span class="pl-s1">metric</span> <span class="pl-c1">=</span> <span class="pl-s">'accuracy'</span>)</pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Model Prediction and Evaluation</h2><a id="user-content-model-prediction-and-evaluation" class="anchor" aria-label="Permalink: Model Prediction and Evaluation" href="#model-prediction-and-evaluation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Prediction and evaluation behave similarly to SciKit-Learn. pyBKT offers a variety of features for prediction and evaluation.</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="from pyBKT.models import Model
# Initialize the model with an optional seed
model = Model(seed = 42, num_fits = 1)
# Load the Cognitive Tutor data (not necessary, but shown
# for the purposes of the tutorial that pyBKT accepts
# DataFrames as well as file locations!).
ct_df = pd.read_csv('ct.csv', encoding = 'latin')
# Train a simple BKT model on all skills in the CT dataset
model.fit(data_path = 'ct.csv')
# Predict on all skills on the training data.
# This returns a Pandas DataFrame.
preds_df = model.predict(data_path = 'ct.csv')
# Evaluate the RMSE of the model on the training data.
# Note that the default evaluate metric is RMSE.
training_rmse = model.evaluate(data = ct_df)
# Evaluate the AUC of the model on the training data. The supported
# metrics are AUC, RMSE and accuracy (they should be lowercased in
# the argument!).
training_auc = model.evaluate(data_path = 'ct.csv', metric = 'auc')
# We can define a custom metric as well.
def mae(true_vals, pred_vals):
""" Calculates the mean absolute error. """
return np.mean(np.abs(true_vals - pred_vals))
training_mae = model.evaluate(data_path = 'ct.csv', metric = mae)"><pre><span class="pl-k">from</span> <span class="pl-s1">pyBKT</span>.<span class="pl-s1">models</span> <span class="pl-k">import</span> <span class="pl-v">Model</span>
<span class="pl-c"># Initialize the model with an optional seed</span>
<span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-en">Model</span>(<span class="pl-s1">seed</span> <span class="pl-c1">=</span> <span class="pl-c1">42</span>, <span class="pl-s1">num_fits</span> <span class="pl-c1">=</span> <span class="pl-c1">1</span>)
<span class="pl-c"># Load the Cognitive Tutor data (not necessary, but shown</span>
<span class="pl-c"># for the purposes of the tutorial that pyBKT accepts</span>
<span class="pl-c"># DataFrames as well as file locations!).</span>
<span class="pl-s1">ct_df</span> <span class="pl-c1">=</span> <span class="pl-s1">pd</span>.<span class="pl-c1">read_csv</span>(<span class="pl-s">'ct.csv'</span>, <span class="pl-s1">encoding</span> <span class="pl-c1">=</span> <span class="pl-s">'latin'</span>)
<span class="pl-c"># Train a simple BKT model on all skills in the CT dataset</span>
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>)
<span class="pl-c"># Predict on all skills on the training data.</span>
<span class="pl-c"># This returns a Pandas DataFrame.</span>
<span class="pl-s1">preds_df</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">predict</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>)
<span class="pl-c"># Evaluate the RMSE of the model on the training data.</span>
<span class="pl-c"># Note that the default evaluate metric is RMSE.</span>
<span class="pl-s1">training_rmse</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">evaluate</span>(<span class="pl-s1">data</span> <span class="pl-c1">=</span> <span class="pl-s1">ct_df</span>)
<span class="pl-c"># Evaluate the AUC of the model on the training data. The supported</span>
<span class="pl-c"># metrics are AUC, RMSE and accuracy (they should be lowercased in</span>
<span class="pl-c"># the argument!).</span>
<span class="pl-s1">training_auc</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">evaluate</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">metric</span> <span class="pl-c1">=</span> <span class="pl-s">'auc'</span>)
<span class="pl-c"># We can define a custom metric as well.</span>
<span class="pl-k">def</span> <span class="pl-en">mae</span>(<span class="pl-s1">true_vals</span>, <span class="pl-s1">pred_vals</span>):
<span class="pl-s">""" Calculates the mean absolute error. """</span>
<span class="pl-k">return</span> <span class="pl-s1">np</span>.<span class="pl-c1">mean</span>(<span class="pl-s1">np</span>.<span class="pl-c1">abs</span>(<span class="pl-s1">true_vals</span> <span class="pl-c1">-</span> <span class="pl-s1">pred_vals</span>))
<span class="pl-s1">training_mae</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">evaluate</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">metric</span> <span class="pl-c1">=</span> <span class="pl-s1">mae</span>)</pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Crossvalidation</h2><a id="user-content-crossvalidation" class="anchor" aria-label="Permalink: Crossvalidation" href="#crossvalidation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Crossvalidation is offered as a blackbox function similar to a combination of fit and evaluate that accepts a particular number of folds, a seed, and a metric (either one of the 3 provided that are 'rmse', 'auc' or 'accuracy' or a custom Python function taking 2 arguments). Similar arguments for the model types, data path/data, and skill names are accepted as with the fit function.</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="from pyBKT.models import Model
# Initialize the model with an optional seed
model = Model(seed = 42, num_fits = 1)
# Crossvalidate with 5 folds on all skills in the CT dataset.
crossvalidated_errors = model.crossvalidate(data_path = 'ct.csv', folds = 5)
# Crossvalidate on a particular set of skills with a given
# seed, folds and metric.
def mae(true_vals, pred_vals):
""" Calculates the mean absolute error. """
return np.mean(np.abs(true_vals - pred_vals))
# Note that the skills argument accepts a REGEX pattern. In this case, this matches and
# crossvalidates on all skills containing the word fraction.
crossvalidated_mae_errs = model.crossvalidate(data_path = 'ct.csv', skills = ".*fraction.*",
folds = 10, metric = mae)
# Crossvalidate using multiple model variants.
crossvalidated_multigsf = model.crossvalidate(data_path = 'ct.csv', multigs = True, forgets = True)"><pre><span class="pl-k">from</span> <span class="pl-s1">pyBKT</span>.<span class="pl-s1">models</span> <span class="pl-k">import</span> <span class="pl-v">Model</span>
<span class="pl-c"># Initialize the model with an optional seed</span>
<span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-en">Model</span>(<span class="pl-s1">seed</span> <span class="pl-c1">=</span> <span class="pl-c1">42</span>, <span class="pl-s1">num_fits</span> <span class="pl-c1">=</span> <span class="pl-c1">1</span>)
<span class="pl-c"># Crossvalidate with 5 folds on all skills in the CT dataset.</span>
<span class="pl-s1">crossvalidated_errors</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">crossvalidate</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">folds</span> <span class="pl-c1">=</span> <span class="pl-c1">5</span>)
<span class="pl-c"># Crossvalidate on a particular set of skills with a given </span>
<span class="pl-c"># seed, folds and metric.</span>
<span class="pl-k">def</span> <span class="pl-en">mae</span>(<span class="pl-s1">true_vals</span>, <span class="pl-s1">pred_vals</span>):
<span class="pl-s">""" Calculates the mean absolute error. """</span>
<span class="pl-k">return</span> <span class="pl-s1">np</span>.<span class="pl-c1">mean</span>(<span class="pl-s1">np</span>.<span class="pl-c1">abs</span>(<span class="pl-s1">true_vals</span> <span class="pl-c1">-</span> <span class="pl-s1">pred_vals</span>))
<span class="pl-c"># Note that the skills argument accepts a REGEX pattern. In this case, this matches and </span>
<span class="pl-c"># crossvalidates on all skills containing the word fraction.</span>
<span class="pl-s1">crossvalidated_mae_errs</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">crossvalidate</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span> <span class="pl-c1">=</span> <span class="pl-s">".*fraction.*"</span>,
<span class="pl-s1">folds</span> <span class="pl-c1">=</span> <span class="pl-c1">10</span>, <span class="pl-s1">metric</span> <span class="pl-c1">=</span> <span class="pl-s1">mae</span>)
<span class="pl-c"># Crossvalidate using multiple model variants.</span>
<span class="pl-s1">crossvalidated_multigsf</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>.<span class="pl-c1">crossvalidate</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">multigs</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>, <span class="pl-s1">forgets</span> <span class="pl-c1">=</span> <span class="pl-c1">True</span>)</pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Roster</h2><a id="user-content-roster" class="anchor" aria-label="Permalink: Roster" href="#roster"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">The model has been extended into the Roster to accomodate and simulate the learning environment for a cohort of students learning any combination of individual skills. The Roster feature has the efficient ability to track individuals' progress through the mastery and correctness probabilities outputted by BKT by storing only the current latent and observable state of the student. The following shows an example of Roster being used in practise:</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="from pyBKT.models import *
import numpy as np
# Create a backend pyBKT model and fit it on the CT data
model = Model()
model.fit(data_path = 'ct.csv')
# Create a Roster with two students, Jeff and Bob, who are participating in the roster
# for one skill (Calculate Unit Rate) using the pyBKT model above.
roster = Roster(students = ['Jeff', 'Bob'], skills = 'Calculate unit rate', model = model)
# Initial mastery state (prior) for Jeff, should be unmastered with low probability of mastery
# get_state_type returns whether a student has mastered the skill or not
# get_mastery_prob returns the probability a student has mastered the skill
print("Jeff's mastery (t = 0):", roster.get_state_type('Calculate unit rate', 'Jeff'))
print("Jeff's probability of mastery (t = 0):", roster.get_mastery_prob('Calculate unit rate', 'Jeff'))
# We can update Jeff's state by adding one or more responses to a particular skill. In this case,
# we observed a correct response for the one skill in the roster.
jeff_new_state = roster.update_state('Calculate unit rate', 'Jeff', 1)
# Check the updated mastery state and probability.
print("Jeff's mastery (t = 1):", roster.get_state_type('Calculate unit rate', 'Jeff'))
print("Jeff's probability of mastery (t = 1):", roster.get_mastery_prob('Calculate unit rate', 'Jeff'))
# We can update his state with multiple correct responses (ten of them).
roster.update_state('Calculate unit rate', 'Jeff', np.ones(10))
# After 10 consecutive correct responses, he should have mastered the skill.
print("Jeff's mastery (t = 11):", roster.get_state_type('Calculate unit rate', 'Jeff'))
print("Jeff's probability of mastery (t = 11):", roster.get_mastery_prob('Calculate unit rate', 'Jeff'))
# Programmatically check whether he has mastered the skill
if roster.get_state_type('Calculate unit rate', 'Jeff') == StateType.MASTERED:
print("Jeff has mastered the skill!")
# We can update Bob's state with two correct responses.
roster.update_state('Calculate unit rate', 'Bob', np.ones(2))
# He should remain unmastered.
print("Bob's mastery (t = 2):", roster.get_state_type('Calculate unit rate', 'Bob'))
print("Bob's probability of mastery (t = 2):", roster.get_mastery_prob('Calculate unit rate', 'Bob'))
# We can print aggregate statistics for mastery and correctness.
print("Both students' probabilites of correctness:", roster.get_correct_probs('Calculate unit rate'))
print("Both students' probabilites of mastery:", roster.get_mastery_probs('Calculate unit rate'))
# Add a new student, Sarah.
roster.add_student('Calculate unit rate', 'Sarah')
# Update Sarah's state with a sequence of correct and incorrect responses.
sarah_new_state = roster.update_state('Calculate unit rate', 'Sarah', np.array([1, 0, 1, 0, 1, 1, 1]))
# Print Sarah's correctness and mastery probability.
print("Sarah's correctness probability:", sarah_new_state.get_correct_prob()
print("Sarah's mastery probability:", sarah_new_state.get_mastery_prob())
# Delete Bob from the roster.
roster.remove_student('Calculate unit rate', 'Bob')
# Reset student's state (i.e. latent and observable).
roster.reset_state('Calculate unit rate', 'Jeff')
# Jeff should be back to the initial prior as the mastery probability and should be unmastered.
print("Jeff's mastery (t' = 0):", roster.get_state_type('Calculate unit rate', 'Jeff'))
print("Jeff's probability of mastery (t' = 0):", roster.get_mastery_prob('Calculate unit rate', 'Jeff'))
"><pre><span class="pl-k">from</span> <span class="pl-s1">pyBKT</span>.<span class="pl-s1">models</span> <span class="pl-k">import</span> <span class="pl-c1">*</span>
<span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span>
<span class="pl-c"># Create a backend pyBKT model and fit it on the CT data</span>
<span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-en">Model</span>()
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>)
<span class="pl-c"># Create a Roster with two students, Jeff and Bob, who are participating in the roster</span>
<span class="pl-c"># for one skill (Calculate Unit Rate) using the pyBKT model above.</span>
<span class="pl-s1">roster</span> <span class="pl-c1">=</span> <span class="pl-en">Roster</span>(<span class="pl-s1">students</span> <span class="pl-c1">=</span> [<span class="pl-s">'Jeff'</span>, <span class="pl-s">'Bob'</span>], <span class="pl-s1">skills</span> <span class="pl-c1">=</span> <span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-s1">model</span>)
<span class="pl-c"># Initial mastery state (prior) for Jeff, should be unmastered with low probability of mastery</span>
<span class="pl-c"># get_state_type returns whether a student has mastered the skill or not</span>
<span class="pl-c"># get_mastery_prob returns the probability a student has mastered the skill</span>
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's mastery (t = 0):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's probability of mastery (t = 0):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_prob</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-c"># We can update Jeff's state by adding one or more responses to a particular skill. In this case,</span>
<span class="pl-c"># we observed a correct response for the one skill in the roster.</span>
<span class="pl-s1">jeff_new_state</span> <span class="pl-c1">=</span> <span class="pl-s1">roster</span>.<span class="pl-c1">update_state</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>, <span class="pl-c1">1</span>)
<span class="pl-c"># Check the updated mastery state and probability.</span>
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's mastery (t = 1):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's probability of mastery (t = 1):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_prob</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-c"># We can update his state with multiple correct responses (ten of them).</span>
<span class="pl-s1">roster</span>.<span class="pl-c1">update_state</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>, <span class="pl-s1">np</span>.<span class="pl-c1">ones</span>(<span class="pl-c1">10</span>))
<span class="pl-c"># After 10 consecutive correct responses, he should have mastered the skill.</span>
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's mastery (t = 11):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-en">print</span>(<span class="pl-s">"Jeff's probability of mastery (t = 11):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_prob</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-c"># Programmatically check whether he has mastered the skill</span>
<span class="pl-k">if</span> <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>) <span class="pl-c1">==</span> <span class="pl-v">StateType</span>.<span class="pl-c1">MASTERED</span>:
<span class="pl-en">print</span>(<span class="pl-s">"Jeff has mastered the skill!"</span>)
<span class="pl-c"># We can update Bob's state with two correct responses.</span>
<span class="pl-s1">roster</span>.<span class="pl-c1">update_state</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Bob'</span>, <span class="pl-s1">np</span>.<span class="pl-c1">ones</span>(<span class="pl-c1">2</span>))
<span class="pl-c"># He should remain unmastered.</span>
<span class="pl-en">print</span>(<span class="pl-s">"Bob's mastery (t = 2):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Bob'</span>))
<span class="pl-en">print</span>(<span class="pl-s">"Bob's probability of mastery (t = 2):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_prob</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Bob'</span>))
<span class="pl-c"># We can print aggregate statistics for mastery and correctness.</span>
<span class="pl-en">print</span>(<span class="pl-s">"Both students' probabilites of correctness:"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_correct_probs</span>(<span class="pl-s">'Calculate unit rate'</span>))
<span class="pl-en">print</span>(<span class="pl-s">"Both students' probabilites of mastery:"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_probs</span>(<span class="pl-s">'Calculate unit rate'</span>))
<span class="pl-c"># Add a new student, Sarah.</span>
<span class="pl-s1">roster</span>.<span class="pl-c1">add_student</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Sarah'</span>)
<span class="pl-c"># Update Sarah's state with a sequence of correct and incorrect responses.</span>
<span class="pl-s1">sarah_new_state</span> <span class="pl-c1">=</span> <span class="pl-s1">roster</span>.<span class="pl-c1">update_state</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Sarah'</span>, <span class="pl-s1">np</span>.<span class="pl-c1">array</span>([<span class="pl-c1">1</span>, <span class="pl-c1">0</span>, <span class="pl-c1">1</span>, <span class="pl-c1">0</span>, <span class="pl-c1">1</span>, <span class="pl-c1">1</span>, <span class="pl-c1">1</span>]))
<span class="pl-c"># Print Sarah's correctness and mastery probability.</span>
<span class="pl-k">print</span>(<span class="pl-s">"Sarah's correctness probability:"</span>, <span class="pl-s1">sarah_new_state</span>.<span class="pl-c1">get_correct_prob</span>()
<span class="pl-s1">print</span>(<span class="pl-s">"Sarah's mastery probability:"</span>, <span class="pl-s1">sarah_new_state</span>.<span class="pl-c1">get_mastery_prob</span>())
<span class="pl-c"># Delete Bob from the roster.</span>
<span class="pl-s1">roster</span>.<span class="pl-c1">remove_student</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Bob'</span>)
<span class="pl-c"># Reset student's state (i.e. latent and observable).</span>
<span class="pl-s1">roster</span>.<span class="pl-c1">reset_state</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>)
<span class="pl-c"># Jeff should be back to the initial prior as the mastery probability and should be unmastered.</span>
<span class="pl-s1">print</span>(<span class="pl-s">"Jeff's mastery (t' = 0):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_state_type</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))
<span class="pl-s1">print</span>(<span class="pl-s">"Jeff's probability of mastery (t' = 0):"</span>, <span class="pl-s1">roster</span>.<span class="pl-c1">get_mastery_prob</span>(<span class="pl-s">'Calculate unit rate'</span>, <span class="pl-s">'Jeff'</span>))</pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Parameter Fixing</h2><a id="user-content-parameter-fixing" class="anchor" aria-label="Permalink: Parameter Fixing" href="#parameter-fixing"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Another advanced feature supported by pyBKT is parameter fixing, where we can fix one or more parameters and train the model conditioned on those fixed parameters. This can be useful if you already know the ground truth value of some parameters beforehand, or to avoid degenerate model creation by fixing parameters at reasonable values. To specify which parameters and values we want fixed for any skill, we can pass in a dictionary to model.coef_, and then specify fixed=True in the model.fit call:</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="from pyBKT.models import *
import numpy as np
model = Model()
# Fixes the prior rate and learn rate to 0.1 for the Plot imperfect radical skill, and trains the model given those fixed parameters.
model.coef_ = {'Plot imperfect radical': {'prior': 0.1, 'learns': np.array([0.1])}}
model.fit(data_path = 'ct.csv', skills='Plot imperfect radical', fixed=True)
model.params()"><pre><span class="pl-k">from</span> <span class="pl-s1">pyBKT</span>.<span class="pl-s1">models</span> <span class="pl-k">import</span> <span class="pl-c1">*</span>
<span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span>
<span class="pl-s1">model</span> <span class="pl-c1">=</span> <span class="pl-en">Model</span>()
<span class="pl-c"># Fixes the prior rate and learn rate to 0.1 for the Plot imperfect radical skill, and trains the model given those fixed parameters.</span>
<span class="pl-s1">model</span>.<span class="pl-c1">coef_</span> <span class="pl-c1">=</span> {<span class="pl-s">'Plot imperfect radical'</span>: {<span class="pl-s">'prior'</span>: <span class="pl-c1">0.1</span>, <span class="pl-s">'learns'</span>: <span class="pl-s1">np</span>.<span class="pl-c1">array</span>([<span class="pl-c1">0.1</span>])}}
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span><span class="pl-c1">=</span><span class="pl-s">'Plot imperfect radical'</span>, <span class="pl-s1">fixed</span><span class="pl-c1">=</span><span class="pl-c1">True</span>)
<span class="pl-s1">model</span>.<span class="pl-c1">params</span>()</pre></div>
<p dir="auto">Within the model.coef_ dictionary, the 'prior' parameter takes a scalar, while 'learns', 'forgets', 'guesses', and 'slips' takes an np.array, in order to provide support for parameter fixing in model extensions with multiple learn or guess classes. An example of such is shown below.</p>
<div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="# The Plot pi skill has 10 different guess/slip classes. This is how you would fix those slip classes to 0, 0.1, ..., 0.9 and train the model conditioned on those slip values.
model.coef_ = {'Plot pi': {'slips': np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])}}
model.fit(data_path = 'ct.csv', skills='Plot pi', multigs=True, fixed=True)
model.params()"><pre><span class="pl-c"># The Plot pi skill has 10 different guess/slip classes. This is how you would fix those slip classes to 0, 0.1, ..., 0.9 and train the model conditioned on those slip values.</span>
<span class="pl-s1">model</span>.<span class="pl-c1">coef_</span> <span class="pl-c1">=</span> {<span class="pl-s">'Plot pi'</span>: {<span class="pl-s">'slips'</span>: <span class="pl-s1">np</span>.<span class="pl-c1">array</span>([<span class="pl-c1">0</span>, <span class="pl-c1">0.1</span>, <span class="pl-c1">0.2</span>, <span class="pl-c1">0.3</span>, <span class="pl-c1">0.4</span>, <span class="pl-c1">0.5</span>, <span class="pl-c1">0.6</span>, <span class="pl-c1">0.7</span>, <span class="pl-c1">0.8</span>, <span class="pl-c1">0.9</span>])}}
<span class="pl-s1">model</span>.<span class="pl-c1">fit</span>(<span class="pl-s1">data_path</span> <span class="pl-c1">=</span> <span class="pl-s">'ct.csv'</span>, <span class="pl-s1">skills</span><span class="pl-c1">=</span><span class="pl-s">'Plot pi'</span>, <span class="pl-s1">multigs</span><span class="pl-c1">=</span><span class="pl-c1">True</span>, <span class="pl-s1">fixed</span><span class="pl-c1">=</span><span class="pl-c1">True</span>)
<span class="pl-s1">model</span>.<span class="pl-c1">params</span>()</pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Extended Features</h2><a id="user-content-extended-features" class="anchor" aria-label="Permalink: Extended Features" href="#extended-features"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">Extended features include model parameter initialization by setting model.coef_, providing a configuration dictionary, setting model default columns, and more. For more information about these features, take a look at the Colab notebook provided at the top of the README.</p>
<div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Internal Data Format</h1><a id="user-content-internal-data-format" class="anchor" aria-label="Permalink: Internal Data Format" href="#internal-data-format"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto"><em>pyBKT</em> models student mastery of a skills as they progress through series of learning resources and checks for understanding. Mastery is modelled as a latent variable has two states - "knowing" and "not knowing". At each checkpoint, students may be given a learning resource (i.e. watch a video) and/or question(s) to check for understanding. The model finds the probability of learning, forgetting, slipping and guessing that maximizes the likelihood of observed student responses to questions.</p>
<p dir="auto">To run the pyBKT model, define the following variables:</p>
<ul dir="auto">
<li><code>num_subparts</code>: The number of unique questions used to check understanding. Each subpart has a unique set of emission probabilities.</li>
<li><code>num_resources</code>: The number of unique learning resources available to students.</li>
<li><code>num_fit_initialization</code>: The number of iterations in the EM step.</li>
</ul>
<p dir="auto">Next, create an input object <code>Data</code>, containing the following attributes:</p>
<ul dir="auto">
<li>
<p dir="auto"><code>data</code>: a matrix containing sequential checkpoints for all students, with their responses. Each row represents a different subpart, and each column a checkpoint for a student. There are three potential values: {0 = no response or no question asked, 1 = wrong response, 2 = correct response}. If at a checkpoint, a resource was given but no question asked, the associated column would have <code>0</code> values in all rows. For example, to set up data containing 5 subparts given to two students over 2-3 checkpoints, the matrix would look as follows:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" | 0 0 0 0 2 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 2 0 0 | "><pre class="notranslate"><code> | 0 0 0 0 2 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 2 0 0 |
</code></pre></div>
<p dir="auto">In the above example, the first student starts out with just a learning resource, and no checks for understanding. In subsequent checkpoints, this student also responds to subpart 2 and 5, and gets the first wrong and the second correct.</p>
</li>
<li>
<p dir="auto"><code>starts</code>: defines each student's starting column on the <code>data</code> matrix. For the above matrix, <code>starts</code> would be defined as:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" | 1 4 |"><pre class="notranslate"><code> | 1 4 |
</code></pre></div>
</li>
<li>
<p dir="auto"><code>lengths</code>: defines the number of check point for each student. For the above matrix, <code>lengths</code> would be defined as:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" | 3 2 |"><pre class="notranslate"><code> | 3 2 |
</code></pre></div>
</li>
<li>
<p dir="auto"><code>resources</code>: defines the sequential id of the resources at each checkpoint. Each position in the vector corresponds to the column in the <code>data</code> matrix. For the above matrix, the learning <code>resources</code> at each checkpoint would be structured as:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" | 1 2 1 1 3 |"><pre class="notranslate"><code> | 1 2 1 1 3 |
</code></pre></div>
</li>
<li>
<p dir="auto"><code>stateseqs</code>: this attribute is the true knowledge state for above data and should be left undefined before running the <code>pyBKT</code> model.</p>
</li>
</ul>
<p dir="auto">The output of the model can will be stored in a <code>fitmodel</code> object, containing the following probabilities as attributes:</p>
<ul dir="auto">
<li><code>As</code>: the transition probability between the "knowing" and "not knowing" state. Includes both the <code>learns</code> and <code>forgets</code> probabilities, and their inverse. <code>As</code> creates a separate transition probability for each resource.</li>
<li><code>learns</code>: the probability of transitioning to the "knowing" state given "not known".</li>
<li><code>forgets</code>: the probability of transitioning to the "not knowing" state given "known".</li>
<li><code>prior</code>: the prior probability of "knowing".</li>
</ul>
<p dir="auto">The <code>fitmodel</code> also includes the following emission probabilities:</p>
<ul dir="auto">
<li><code>guesses</code>: the probability of guessing correctly, given "not knowing" state.</li>
<li><code>slips</code>: the probability of picking incorrect answer, given "knowing" state.</li>
</ul>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Citation</h2><a id="user-content-citation" class="anchor" aria-label="Permalink: Citation" href="#citation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<p dir="auto">To credit this library, please cite our paper published in the Educaitonal Data Mining Conference:</p>
<p dir="auto">Badrinath, A., Wang, F., Pardos, Z.A. (2021) pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models. In S. Hsiao, & S. Sahebi (Eds.) <em>Proceedings of the 14th International Conference on Educational Data Mining</em> (EDM). Pages 468-474.</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="@inproceedings{badrinath2021pybkt,
title={pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models},
author={Badrinath, Anirudhan and Wang, Frederic and Pardos, Zachary},
booktitle={Proceedings of the 14th International Conference on Educational Data Mining},
pages={468--474},
year={2021}
}"><pre class="notranslate"><code>@inproceedings{badrinath2021pybkt,
title={pyBKT: An Accessible Python Library of Bayesian Knowledge Tracing Models},
author={Badrinath, Anirudhan and Wang, Frederic and Pardos, Zachary},
booktitle={Proceedings of the 14th International Conference on Educational Data Mining},
pages={468--474},
year={2021}
}
</code></pre></div>
<div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">TODOs</h2><a id="user-content-todos" class="anchor" aria-label="Permalink: TODOs" href="#todos"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div>
<ul dir="auto">
<li>Exporting compiled binaries on PyPi</li>
<li>Additional model variants</li>
</ul>
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Python implementation of Bayesian Knowledge Tracing and extensions
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<include-fragment src="/CAHLR/pyBKT/used_by_list" accept="text/fragment+html" data-nonce="3b4b5756-6ace-4015-d06e-046f3fa37eae" data-view-component="true">
</include-fragment>
</div>
</div>
<div class="BorderGrid-row">
<div class="BorderGrid-cell">
<h2 class="h4 mb-3">
<a href="/CAHLR/pyBKT/graphs/contributors" data-view-component="true" class="Link--primary no-underline Link d-flex flex-items-center">Contributors
<span title="10" data-view-component="true" class="Counter ml-1">10</span></a></h2>
<ul class="list-style-none d-flex flex-wrap mb-n2">
<li class="mb-2 mr-2"
>
<a href="https://github.com/abadrinath947"
class=""
data-hovercard-type="user" data-hovercard-url="/users/abadrinath947/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/40471069?s=64&v=4" alt="@abadrinath947" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/zpardos"
class=""
data-hovercard-type="user" data-hovercard-url="/users/zpardos/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/1536150?s=64&v=4" alt="@zpardos" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/fredwang25"
class=""
data-hovercard-type="user" data-hovercard-url="/users/fredwang25/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/31838843?s=64&v=4" alt="@fredwang25" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/cagaray"
class=""
data-hovercard-type="user" data-hovercard-url="/users/cagaray/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/14813651?s=64&v=4" alt="@cagaray" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/themrzmaster"
class=""
data-hovercard-type="user" data-hovercard-url="/users/themrzmaster/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/852747?s=64&v=4" alt="@themrzmaster" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/gtfierro"
class=""
data-hovercard-type="user" data-hovercard-url="/users/gtfierro/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/55434?s=64&v=4" alt="@gtfierro" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/rachelcusack"
class=""
data-hovercard-type="user" data-hovercard-url="/users/rachelcusack/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/49796187?s=64&v=4" alt="@rachelcusack" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/ahaim5357"
class=""
data-hovercard-type="user" data-hovercard-url="/users/ahaim5357/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/54476145?s=64&v=4" alt="@ahaim5357" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/ShailenSmith"
class=""
data-hovercard-type="user" data-hovercard-url="/users/ShailenSmith/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/66018162?s=64&v=4" alt="@ShailenSmith" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
<li class="mb-2 mr-2"
>
<a href="https://github.com/TijlE-1951707"
class=""
data-hovercard-type="user" data-hovercard-url="/users/TijlE-1951707/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self"
>
<img src="https://avatars.githubusercontent.com/u/72065191?s=64&v=4" alt="@TijlE-1951707" size="32" height="32" width="32" data-view-component="true" class="avatar circle" />
</a>
</li>
</ul>
</div>
</div>
<div class="BorderGrid-row">
<div class="BorderGrid-cell">
<h2 class="h4 mb-3">Languages</h2>
<div class="mb-2">
<span data-view-component="true" class="Progress">
<span style="background-color:#f34b7d !important;;width: 80.2%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#4d41b1 !important;;width: 11.5%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#DA3434 !important;;width: 2.8%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#555555 !important;;width: 2.2%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#3572A5 !important;;width: 1.9%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#3A4E3A !important;;width: 1.1%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
<span style="background-color:#ededed !important;;width: 0.3%;" itemprop="keywords" data-view-component="true" class="Progress-item color-bg-success-emphasis"></span>
</span></div>
<ul class="list-style-none">
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=c%2B%2B" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#f34b7d;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">C++</span>
<span>80.2%</span>
</a>
</li>
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=fortran" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#4d41b1;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">Fortran</span>
<span>11.5%</span>
</a>
</li>
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=cmake" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#DA3434;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">CMake</span>
<span>2.8%</span>
</a>
</li>
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=c" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#555555;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">C</span>
<span>2.2%</span>
</a>
</li>
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=python" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#3572A5;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">Python</span>
<span>1.9%</span>
</a>
</li>
<li class="d-inline">
<a class="d-inline-flex flex-items-center flex-nowrap Link--secondary no-underline text-small mr-3" href="/CAHLR/pyBKT/search?l=cuda" data-ga-click="Repository, language stats search click, location:repo overview">
<svg style="color:#3A4E3A;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">Cuda</span>
<span>1.1%</span>
</a>
</li>
<li class="d-inline">
<span class="d-inline-flex flex-items-center flex-nowrap text-small mr-3">
<svg style="color:#ededed;" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-dot-fill mr-2">
<path d="M8 4a4 4 0 1 1 0 8 4 4 0 0 1 0-8Z"></path>
</svg>
<span class="color-fg-default text-bold mr-1">Other</span>
<span>0.3%</span>
</span>
</li>
</ul>
</div>
</div>
</div>
</div>
</div></div>
</div>
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<button
type="button"
class="Link--secondary underline-on-hover border-0 p-0 color-bg-transparent"
data-action="click:cookie-consent-link#showConsentManagement"
data-analytics-event="{"location":"footer","action":"cookies","context":"subfooter","tag":"link","label":"cookies_link_subfooter_footer"}"
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<button
type="button"
class="Link--secondary underline-on-hover border-0 p-0 color-bg-transparent"
data-action="click:cookie-consent-link#showConsentManagement"
data-analytics-event="{"location":"footer","action":"dont_share_info","context":"subfooter","tag":"link","label":"dont_share_info_link_subfooter_footer"}"
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Do not share my personal information
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<ghcc-consent id="ghcc" class="position-fixed bottom-0 left-0" style="z-index: 999999" data-initial-cookie-consent-allowed="" data-cookie-consent-required="true"></ghcc-consent>
<div id="ajax-error-message" class="ajax-error-message flash flash-error" hidden>
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<path d="M6.457 1.047c.659-1.234 2.427-1.234 3.086 0l6.082 11.378A1.75 1.75 0 0 1 14.082 15H1.918a1.75 1.75 0 0 1-1.543-2.575Zm1.763.707a.25.25 0 0 0-.44 0L1.698 13.132a.25.25 0 0 0 .22.368h12.164a.25.25 0 0 0 .22-.368Zm.53 3.996v2.5a.75.75 0 0 1-1.5 0v-2.5a.75.75 0 0 1 1.5 0ZM9 11a1 1 0 1 1-2 0 1 1 0 0 1 2 0Z"></path>
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<button type="button" class="flash-close js-ajax-error-dismiss" aria-label="Dismiss error">
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You can’t perform that action at this time.
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<template id="site-details-dialog">
<details class="details-reset details-overlay details-overlay-dark lh-default color-fg-default hx_rsm" open>
<summary role="button" aria-label="Close dialog"></summary>
<details-dialog class="Box Box--overlay d-flex flex-column anim-fade-in fast hx_rsm-dialog hx_rsm-modal">
<button class="Box-btn-octicon m-0 btn-octicon position-absolute right-0 top-0" type="button" aria-label="Close dialog" data-close-dialog>
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x">
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</svg>
</button>
<div class="octocat-spinner my-6 js-details-dialog-spinner"></div>
</details-dialog>
</details>
</template>
<div class="Popover js-hovercard-content position-absolute" style="display: none; outline: none;">
<div class="Popover-message Popover-message--bottom-left Popover-message--large Box color-shadow-large" style="width:360px;">
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<template id="snippet-clipboard-copy-button">
<div class="zeroclipboard-container position-absolute right-0 top-0">
<clipboard-copy aria-label="Copy" class="ClipboardButton btn js-clipboard-copy m-2 p-0" data-copy-feedback="Copied!" data-tooltip-direction="w">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2">
<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path>
</svg>
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2">
<path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path>
</svg>
</clipboard-copy>
</div>
</template>
<template id="snippet-clipboard-copy-button-unpositioned">
<div class="zeroclipboard-container">
<clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w">
<svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon">
<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path>
</svg>
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<path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path>
</svg>
</clipboard-copy>
</div>
</template>
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Whois info of domain
Domain Name: PYBKT.COM
Registry Domain ID: 2677279021_DOMAIN_COM-VRSN
Registrar WHOIS Server: whois.godaddy.com
Registrar URL: http://www.godaddy.com
Updated Date: 2022-10-03T00:53:15Z
Creation Date: 2022-02-23T19:52:35Z
Registry Expiry Date: 2027-02-23T19:52:35Z
Registrar: GoDaddy.com, LLC
Registrar IANA ID: 146
Registrar Abuse Contact Email: [email protected]
Registrar Abuse Contact Phone: 480-624-2505
Domain Status: clientDeleteProhibited https://icann.org/epp#clientDeleteProhibited
Domain Status: clientRenewProhibited https://icann.org/epp#clientRenewProhibited
Domain Status: clientTransferProhibited https://icann.org/epp#clientTransferProhibited
Domain Status: clientUpdateProhibited https://icann.org/epp#clientUpdateProhibited
Name Server: NS75.DOMAINCONTROL.COM
Name Server: NS76.DOMAINCONTROL.COM
DNSSEC: unsigned
URL of the ICANN Whois Inaccuracy Complaint Form: https://www.icann.org/wicf/
>>> Last update of whois database: 2025-05-01T09:44:48Z <<<
For more information on Whois status codes, please visit https://icann.org/epp
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