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Confidence Intervals in Machine Learning | Deepgram

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class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060023-speech-to-speech.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dVEgqo">Voice Agent API</span><span font-size="textXs" class="sc-b323b31-0 sc-3618c394-14 lnJhVG cFsKfJ">For real-time AI Agents</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC bGaVbc"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/product/text-to-speech"><div class="sc-ace17a57-0 gCajMv"><div class="sc-ace17a57-0 sc-3618c394-4 ftcNci bpvjgx"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" 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MuiButton-colorSecondary MuiButton-root MuiButton-text MuiButton-textSecondary MuiButton-sizeSmall MuiButton-textSizeSmall MuiButton-colorSecondary sc-d74559df-0 fqnlbI sc-6e03a9e4-0 iumJHL sc-3618c394-0 gxydGy css-6n9fb7" tabindex="0" type="button" __typename="ComponentCallToActionRecord" id="Xho9X9_YQj2HBRVr87BG0g" href="/learn?type=Article&amp;page=1&amp;category=Announcements"><span class="sc-b323b31-0 fcPowg button-label" display="inline-flex"><span>View more</span></span><style data-emotion="css kcxyz4">.css-kcxyz4{display:inherit;margin-right:-2px;margin-left:8px;}.css-kcxyz4>*:nth-of-type(1){font-size:18px;}</style><span class="MuiButton-icon MuiButton-endIcon MuiButton-iconSizeSmall css-kcxyz4"><div width="fit-content" class="sc-ace17a57-0 ddioGD"><span display="inline-flex" class="sc-b323b31-0 bZmEHx"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" height="16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="M438.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L338.8 224 32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l306.7 0L233.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l160-160z"></path></svg></span></div></span></a></div><div class="sc-ace17a57-0 gzWdaa"><a rel="" target="" display="-webkit-box" height="100%" width="100%" class="sc-e69ac761-0 ecplwP sc-2850a57f-3 cPKdIq" href="/learn/introducing-nova-3-speech-to-text-api"><div width="100%" height="100%" id="e1wy33mNTlGk8-WqDH28_Q" class="sc-ace17a57-0 sc-2850a57f-1 fJWxEy ggobuO"><div width="100%" height="150px" class="sc-6293d692-0 eWcIvK"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="Introducing Nova-3: Setting a New Standard for AI-Driven Speech-to-Text" loading="lazy" width="590" height="259" decoding="async" data-nimg="1" class="sc-2850a57f-2 dSsmQU" style="color:transparent;object-fit:cover" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&amp;w=640&amp;q=75 1x, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&amp;w=1200&amp;q=75 2x" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&amp;w=1200&amp;q=75"/></div></div><div class="sc-ace17a57-0 biWqHE"><span font-weight="semiBold" class="sc-b323b31-0 iNRMrC"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 320 512" color="#ffffff" class="sc-2850a57f-0 Tcnof" style="color:#ffffff" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M285.476 272.971L91.132 467.314c-9.373 9.373-24.569 9.373-33.941 0l-22.667-22.667c-9.357-9.357-9.375-24.522-.04-33.901L188.505 256 34.484 101.255c-9.335-9.379-9.317-24.544.04-33.901l22.667-22.667c9.373-9.373 24.569-9.373 33.941 0L285.475 239.03c9.373 9.372 9.373 24.568.001 33.941z"></path></svg>Introducing Nova-3: Setting a New Standard for AI-Driven Speech-to-Text</span><span class="sc-b323b31-0 jUNaqu">Published on 02/12/25</span></div></div></a></div></div></div></div></li><li height="fit-content" width="100%" tabindex="0" class="sc-6293d692-0 hEIHLV"><div width="100%" class="sc-ace17a57-0 gbwWMz"><div height="fit-content" width="100%" class="sc-ace17a57-0 caCSrG"><span font-size="textXl" font-weight="medium" display="block" cursor="pointer" width="100%" class="sc-b323b31-0 kzoxAi">Solutions</span><div transform="rotateX(0deg)" class="sc-ace17a57-0 fxtsZN"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 gYFcFc"><span display="block" width="auto" class="sc-b323b31-0 gIJLbd">Use Cases</span></div><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/contact-centers"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img 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src="https://www.datocms-assets.com/96965/1728060247-medical.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Medical Transcription</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/deepgram-for-voicebots-and-chatbots"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060265-conversational-ai.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Conversational AI</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/speech-analytics"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060282-speech-analytics.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Speech Analytics</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/media-transcription"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060298-media.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Media Transcription</span></div></div></a></div></div></div></div><div class="sc-ace17a57-0 bcBFEg"><a rel="" target="" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK" href="/customers"><div class="sc-ace17a57-0 ldePaW"><div width="28px" height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="Customers" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728060368-user.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO gpxdfo">Customers</span></div></a><a rel="" target="" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK" href="/partners"><div class="sc-ace17a57-0 ldePaW"><div width="28px" height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="Partners" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728060385-people-connect.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO 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src="https://www.datocms-assets.com/96965/1700614421-glossary-icon.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">AI Glossary</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/about"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060599-speech-bubble.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE 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height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="AI Apps" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728060670-grid.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO gpxdfo">AI Apps</span></div></a><a href="https://www.aiminds.com/subscribe" rel="noreferrer noopener" target="_blank" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK"><div class="sc-ace17a57-0 ldePaW"><div width="28px" height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="AI Minds" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728570215-ai-minds-icon-green-duotone.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO gpxdfo">AI Minds</span></div></a><a rel="" target="" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK" href="/ai-voice-generator"><div class="sc-ace17a57-0 ldePaW"><div width="28px" height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="AI Voice Generator" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728060689-podcast.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO gpxdfo">AI Voice Generator</span></div></a><a rel="" target="" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK" href="/free-transcription"><div class="sc-ace17a57-0 ldePaW"><div 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fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a href="https://developers.deepgram.com/documentation/" rel="noreferrer noopener" target="_blank" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060846-documentation.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Documentation</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/learn?type=Article&amp;page=1&amp;category=Tutorials"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060860-tutorials.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Tutorials</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a href="https://status.deepgram.com/" rel="noreferrer noopener" target="_blank" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060872-status.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Status</span></div></div></a></div></div></div></div><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/changelog"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060899-changelog.svg"/></div></div><div class="sc-ace17a57-0 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class="sc-6293d692-0 csGpzP"><div class="sc-ace17a57-0 hhtFqm glossary-content-wrapper"><div class="sc-ace17a57-0 btkfVN"><div class="sc-ace17a57-0 sc-a48d0877-0 dJCIVv zIKHU"><h1 font-size="displaySm" letter-spacing="neg2" font-weight="semiBold" font-family="primaryFont" class="sc-b323b31-0 JYZsj">Confidence Intervals in Machine Learning</h1><div class="sc-ace17a57-0 fJkbQy"><p font-family="bodyFont" class="sc-5159831f-0 GBftN">This article delves deep into the world of confidence intervals within the machine learning landscape. </p></div></div></div><!--$--><div class="sc-ace17a57-0 sc-4e888a2-0 hfDdWp cifBqP"><p class="sc-5159831f-0">Have you ever wondered how machine learning models make predictions with such precision, yet we&#x27;re advised to take these predictions with a grain of uncertainty? In the realm of machine learning, confidence intervals emerge as a beacon of reliability, guiding practitioners through the fog of predictive analytics. A staggering fact: despite the rapid advancements in machine learning methodologies, the interpretation of model outputs often remains a daunting challenge for many. Understanding confidence intervals in machine learning not only demystifies this aspect but also empowers users to gauge the reliability and stability of their models effectively.</p><p class="sc-5159831f-0">This article delves deep into the world of confidence intervals within the machine learning landscape. You&#x27;ll gain a foundational understanding of what confidence intervals are and why they&#x27;re paramount for quantifying the uncertainty of predictions or parameter estimations in machine learning models. From the practical insights shared by Sebastian Raschka to the critical importance of these intervals in evaluating model performance, this piece covers it all. Expect to uncover how confidence intervals provide a statistical basis for making informed decisions, especially when it comes to interpreting the performance of machine learning models in real-world scenarios.</p><p class="sc-5159831f-0">Are you ready to navigate through the intricacies of confidence intervals and unlock new levels of confidence in your machine learning endeavors? Let&#x27;s explore how these statistical techniques not only quantify uncertainty but also illuminate the path to more reliable and generalizable machine learning models.</p><h2 id="what-are-confidence-intervals-in-machine-learning" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg">What are confidence intervals in machine learning</h2><p class="sc-5159831f-0">In the vast expanse of machine learning, confidence intervals stand out as statistical techniques crucial for determining the reliability of an estimate. But what exactly are confidence intervals, and how do they apply to machine learning? Let&#x27;s break it down:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Confidence intervals</span> provide a range within which we expect the true value of a parameter to lie, with a certain level of confidence, typically 95%. This means that if we were to repeat our study multiple times, 95% of the confidence intervals calculated from those studies would contain the true parameter value.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">They play a pivotal role in <span font-weight="bold" class="sc-b323b31-0 caUwZV">quantifying the uncertainty</span> of a prediction or parameter estimation in machine learning models. This quantification is vital for practitioners to assess the stability and reliability of their models.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">A practical explanation on creating confidence intervals around an estimated value in classifiers can be found in <span font-weight="bold" class="sc-b323b31-0 caUwZV">Sebastian Raschka&#x27;s blog</span>. Raschka&#x27;s insights shed light on the methodology and importance of incorporating confidence intervals in machine learning workflows.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Understanding confidence intervals</span> is essential for evaluating the generalizability of a machine learning model to new, unseen data. This insight is invaluable, especially in scenarios where decisions are based on predictions or estimations derived from machine learning models.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">The significance of confidence intervals extends beyond mere statistical measures; they offer insights into the stability and reliability of machine learning models. This enables practitioners to make informed decisions and interpretations regarding the performance of their models.</p></li></li></ul><p class="sc-5159831f-0">In essence, confidence intervals serve as a critical tool in the arsenal of machine learning practitioners, providing a statistical foundation to the often uncertain task of model prediction and parameter estimation.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="Z5su9I_yQ16q7vzUlugSsg"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1472" height="950" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url(&quot;data:image/svg+xml;charset=utf-8,%3Csvg xmlns=&#x27;http://www.w3.org/2000/svg&#x27; viewBox=&#x27;0 0 1472 950&#x27;%3E%3Cfilter id=&#x27;b&#x27; color-interpolation-filters=&#x27;sRGB&#x27;%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3CfeColorMatrix values=&#x27;1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 100 -1&#x27; result=&#x27;s&#x27;/%3E%3CfeFlood x=&#x27;0&#x27; y=&#x27;0&#x27; width=&#x27;100%25&#x27; height=&#x27;100%25&#x27;/%3E%3CfeComposite operator=&#x27;out&#x27; in=&#x27;s&#x27;/%3E%3CfeComposite in2=&#x27;SourceGraphic&#x27;/%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3C/filter%3E%3Cimage width=&#x27;100%25&#x27; height=&#x27;100%25&#x27; x=&#x27;0&#x27; y=&#x27;0&#x27; preserveAspectRatio=&#x27;none&#x27; style=&#x27;filter: url(%23b);&#x27; href=&#x27;/deepgram.jpg&#x27;/%3E%3C/svg%3E&quot;)" sizes="(min-width: 992px) 810px, 100vw" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=640&amp;q=75 640w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=750&amp;q=75 750w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=828&amp;q=75 828w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=1080&amp;q=75 1080w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=1200&amp;q=75 1200w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=1920&amp;q=75 1920w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=2048&amp;q=75 2048w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=3840&amp;q=75 3840w" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718528956-screen-shot-2024-06-16-at-2-09-13-am.png&amp;w=3840&amp;q=75"/></div><div font-size="textSm" font-style="italic" class="sc-6293d692-0 jgEMAk"><!--$--><!--/$--></div></div></p><h2 id="calculating-confidence-intervals-in-machine-learning" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg">Calculating Confidence Intervals in Machine Learning</h2><p class="sc-5159831f-0">The calculation of confidence intervals in machine learning is a nuanced process that blends statistical theory with computational techniques. This section explores the methodologies and mathematical foundations that underpin the calculation of confidence intervals, offering insights into their practical application in machine learning scenarios.</p><h3 id="general-formula-for-calculating-confidence-intervals" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">General Formula for Calculating Confidence Intervals</h3><p class="sc-5159831f-0">The cornerstone of calculating confidence intervals involves a few key components:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Estimated Parameter</span>: This could be any statistic, such as the mean or median, derived from your dataset.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Critical Value</span>: Depending on the confidence level chosen, this value (z-score or t-score) quantifies the degree to which the estimated parameter can vary from the true population parameter.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Standard Error of the Estimate</span>: This measures the dispersion of the sample mean from the population mean.</p></li></li></ul><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">The Formula</span>: Confidence Interval = Estimated Parameter ± (Critical Value * Standard Error)</p><p class="sc-5159831f-0">This formula underpins the creation of confidence intervals across various statistical and machine learning applications, serving as a fundamental tool for quantifying uncertainty.</p><h3 id="bootstrap-method-for-confidence-intervals" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Bootstrap Method for Confidence Intervals</h3><p class="sc-5159831f-0">The bootstrap method, as elaborated on GeeksforGeeks, offers a powerful, non-parametric approach to estimating confidence intervals:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Resampling</span>: This involves randomly selecting observations from the dataset, with replacement, to create multiple samples.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Estimation</span>: For each resampled dataset, calculate the statistic of interest.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Confidence Interval Calculation</span>: Determine the distribution of the estimated statistics and then calculate the desired confidence interval.</p></li></li></ul><p class="sc-5159831f-0">This method is particularly useful in situations where the theoretical distribution of the statistic is unknown or difficult to determine.</p><h3 id="crossvalidation-techniques-for-model-stability" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Cross-Validation Techniques for Model Stability</h3><p class="sc-5159831f-0">Cross-validation plays a crucial role in assessing model stability and calculating confidence intervals for model accuracy. Insights from Junjie Zhang&#x27;s 2019 research highlight how cross-validation can be instrumental:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Model Evaluation</span>: By partitioning the dataset into training and testing sets, cross-validation allows for the evaluation of model performance across multiple subsets of data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Confidence Interval Estimation</span>: Through repeated sampling and testing, confidence intervals for model accuracy can be derived, offering insights into the model&#x27;s generalizability and stability.</p></li></li></ul><h3 id="prediction-intervals-vs-confidence-intervals" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Prediction Intervals vs. Confidence Intervals</h3><p class="sc-5159831f-0">While closely related, prediction intervals and confidence intervals cater to different aspects of uncertainty:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Prediction Intervals</span>: Focus on the uncertainty surrounding individual predictions made by the model.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Confidence Intervals</span>: Aim to quantify the uncertainty around an estimated parameter of the population from which the dataset was sampled.</p></li></li></ul><p class="sc-5159831f-0">Understanding the distinction between these two concepts is crucial for accurate interpretation of model outputs.</p><h3 id="utilizing-statistical-software-and-programming-languages" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Utilizing Statistical Software and Programming Languages</h3><p class="sc-5159831f-0">Python emerges as a leading tool for calculating confidence intervals, with various libraries and online resources enhancing its capability:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Statistical Libraries</span>: Libraries such as <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">SciPy</span> and <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">StatsModels</span> provide built-in functions for calculating confidence intervals efficiently.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Custom Implementation</span>: For more complex models or unique requirements, Python allows for the custom implementation of confidence interval calculations.</p></li></li></ul><p class="sc-5159831f-0">Leveraging these tools streamlines the process of quantifying uncertainty in machine learning models.</p><h3 id="the-impact-of-confidence-level-choices" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">The Impact of Confidence Level Choices</h3><p class="sc-5159831f-0">The choice of confidence level (e.g., 95% or 99%) significantly influences the width of the confidence interval:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Higher Confidence Level</span>: Results in a wider confidence interval, indicating greater uncertainty.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Lower Confidence Level</span>: Leads to a narrower confidence interval, suggesting more precision but potentially overlooking the true parameter value.</p></li></li></ul><p class="sc-5159831f-0">Selecting the appropriate confidence level hinges on the specific context and requirements of the machine learning task at hand, balancing the trade-off between precision and reliability.</p><p class="sc-5159831f-0">By weaving together these methodologies and considerations, machine learning practitioners can effectively calculate confidence intervals, thereby shedding light on the reliability and generalizability of their models. This foundational understanding not only enhances model evaluation but also reinforces decision-making processes in the ever-evolving landscape of machine learning.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="IbSwv5QJQCyBYp86KUZZnA"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1502" height="886" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url(&quot;data:image/svg+xml;charset=utf-8,%3Csvg xmlns=&#x27;http://www.w3.org/2000/svg&#x27; viewBox=&#x27;0 0 1502 886&#x27;%3E%3Cfilter id=&#x27;b&#x27; color-interpolation-filters=&#x27;sRGB&#x27;%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3CfeColorMatrix values=&#x27;1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 100 -1&#x27; result=&#x27;s&#x27;/%3E%3CfeFlood x=&#x27;0&#x27; y=&#x27;0&#x27; width=&#x27;100%25&#x27; height=&#x27;100%25&#x27;/%3E%3CfeComposite operator=&#x27;out&#x27; in=&#x27;s&#x27;/%3E%3CfeComposite in2=&#x27;SourceGraphic&#x27;/%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3C/filter%3E%3Cimage width=&#x27;100%25&#x27; height=&#x27;100%25&#x27; x=&#x27;0&#x27; y=&#x27;0&#x27; preserveAspectRatio=&#x27;none&#x27; style=&#x27;filter: url(%23b);&#x27; href=&#x27;/deepgram.jpg&#x27;/%3E%3C/svg%3E&quot;)" sizes="(min-width: 992px) 810px, 100vw" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=640&amp;q=75 640w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=750&amp;q=75 750w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=828&amp;q=75 828w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=1080&amp;q=75 1080w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=1200&amp;q=75 1200w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=1920&amp;q=75 1920w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=2048&amp;q=75 2048w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=3840&amp;q=75 3840w" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529161-screen-shot-2024-06-16-at-2-12-39-am.png&amp;w=3840&amp;q=75"/></div><div font-size="textSm" font-style="italic" class="sc-6293d692-0 jgEMAk"><!--$--><!--/$--></div></div></p><h2 id="methods-for-creating-confidence-intervals-in-machine-learning" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg">Methods for Creating Confidence Intervals in Machine Learning</h2><p class="sc-5159831f-0">In the realm of machine learning, the creation of confidence intervals is paramount for interpreting the reliability and precision of model predictions and estimates. Various methods, each with its own set of assumptions and implementations, facilitate this process. By delving into the analytical, empirical, and Bayesian methods, as well as the role of simulation studies, this section elucidates the multifaceted approaches to generating confidence intervals in machine learning applications.</p><h3 id="analytical-method" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Analytical Method</h3><p class="sc-5159831f-0">The analytical method for creating confidence intervals hinges on certain assumptions about the distribution of the estimator. Key points include:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Assumption of Normality</span>: This method typically assumes that the estimator follows a normal distribution, a presumption that holds true in many practical scenarios due to the Central Limit Theorem.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Well-understood Estimator Distribution</span>: It is most effective when the distribution of the estimator and its variance are well-characterized and can be analytically described.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Application</span>: Commonly applied in scenarios where the mathematical properties of the estimator are clearly defined, such as mean or variance estimations from large sample sizes.</p></li></li></ul><p class="sc-5159831f-0">This method&#x27;s strength lies in its straightforward applicability and the theoretical backing it provides, offering clear, mathematically derived confidence intervals under well-defined conditions.</p><h3 id="empirical-method" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Empirical Method</h3><p class="sc-5159831f-0">The empirical method, notably the bootstrap technique, offers a flexible approach to estimating confidence intervals without stringent distributional assumptions:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Resampling with Replacement</span>: By creating numerous resampled datasets from the original data and calculating the statistic of interest, the bootstrap method builds an empirical distribution of the estimator.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Distribution Agnostic</span>: This technique does not assume a specific underlying distribution, making it highly adaptable to various types of data and models.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Small Sample Sizes</span>: Particularly beneficial for complex estimators or when dealing with small datasets where traditional analytical methods may falter.</p></li></li></ul><p class="sc-5159831f-0">Reference to the bootstrap confidence interval technique showcases its practical utility in machine learning, highlighting its capacity to handle the uncertainty of predictions in a data-driven manner.</p><h3 id="bayesian-method" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Bayesian Method</h3><p class="sc-5159831f-0">Incorporating prior knowledge and beliefs, the Bayesian method for confidence intervals introduces a probabilistic interpretation to the estimation process:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Prior Information</span>: By integrating prior knowledge about the parameters through a prior distribution, this method refines the estimation process based on observed data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Probabilistic Interpretation</span>: Offers a Bayesian credible interval, which provides a probabilistic range within which the true parameter value is expected to lie, given the observed data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Flexibility</span>: This approach allows for the incorporation of new evidence, updating the confidence (credible) intervals as more data become available.</p></li></li></ul><p class="sc-5159831f-0">The Bayesian method exemplifies the fusion of prior knowledge with empirical data, offering a nuanced approach to quantifying uncertainty in machine learning models.</p><h3 id="role-of-simulation-studies" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Role of Simulation Studies</h3><p class="sc-5159831f-0">Simulation studies play a crucial role in understanding the behavior of confidence intervals under various model assumptions and data scenarios:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Model Assumptions</span>: By simulating data under controlled conditions, researchers can assess how well confidence intervals perform under different model assumptions.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Data Scenarios</span>: Simulation enables the exploration of confidence interval behavior in diverse data conditions, including skewed distributions, outliers, or correlated variables.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Insights and Validation</span>: These studies provide valuable insights into the robustness and reliability of confidence interval methods, guiding the choice of appropriate techniques for specific machine learning problems.</p></li></li></ul><h3 id="software-packages-and-libraries" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Software Packages and Libraries</h3><p class="sc-5159831f-0">The implementation of these methods is facilitated by various software packages and libraries in Python and R, catering to the needs of the machine learning community:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Python Libraries</span>: Tools like <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">SciPy</span> for analytical methods, <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">bootstrapped</span> for the bootstrap technique, and <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">PyMC3</span> for Bayesian approaches enable efficient computation of confidence intervals.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">R Packages</span>: Similar capabilities are available in R, with packages such as <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">boot</span> for bootstrap intervals and <span font-family="secondaryFont" class="sc-b323b31-0 sc-42818e5a-4 hqcSqI jpHeYz">rstan</span> for Bayesian analysis, among others.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Examples from the Community</span>: Both Python and R are widely used in the machine learning community, with numerous examples and tutorials available to guide practitioners in applying these methods to real-world datasets.</p></li></li></ul><h3 id="tradeoffs" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Trade-offs</h3><p class="sc-5159831f-0">When choosing a method for creating confidence intervals in machine learning, several trade-offs must be considered:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Computational Complexity</span>: Empirical and Bayesian methods, while powerful, can be computationally intensive, especially with large datasets or complex models.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Accuracy</span>: The precision of the confidence intervals can vary significantly between methods, influenced by the underlying assumptions and the nature of the data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Interpretability</span>: The ease of interpreting and communicating the results of different methods can affect their suitability for certain applications or audiences.</p></li></li></ul><p class="sc-5159831f-0">By carefully navigating these trade-offs, machine learning practitioners can select the most appropriate method for creating confidence intervals, balancing computational demands with the need for accuracy and interpretability. Through the judicious application of analytical, empirical, and Bayesian methods, alongside insights from simulation studies, the field continues to advance our understanding of uncertainty quantification in machine learning models.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="FaceuzhAQRGLZjVVvAu5fQ"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1492" height="960" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url(&quot;data:image/svg+xml;charset=utf-8,%3Csvg xmlns=&#x27;http://www.w3.org/2000/svg&#x27; viewBox=&#x27;0 0 1492 960&#x27;%3E%3Cfilter id=&#x27;b&#x27; color-interpolation-filters=&#x27;sRGB&#x27;%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3CfeColorMatrix values=&#x27;1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 100 -1&#x27; result=&#x27;s&#x27;/%3E%3CfeFlood x=&#x27;0&#x27; y=&#x27;0&#x27; width=&#x27;100%25&#x27; height=&#x27;100%25&#x27;/%3E%3CfeComposite operator=&#x27;out&#x27; in=&#x27;s&#x27;/%3E%3CfeComposite in2=&#x27;SourceGraphic&#x27;/%3E%3CfeGaussianBlur stdDeviation=&#x27;20&#x27;/%3E%3C/filter%3E%3Cimage width=&#x27;100%25&#x27; height=&#x27;100%25&#x27; x=&#x27;0&#x27; y=&#x27;0&#x27; preserveAspectRatio=&#x27;none&#x27; style=&#x27;filter: url(%23b);&#x27; href=&#x27;/deepgram.jpg&#x27;/%3E%3C/svg%3E&quot;)" sizes="(min-width: 992px) 810px, 100vw" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=640&amp;q=75 640w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=750&amp;q=75 750w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=828&amp;q=75 828w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=1080&amp;q=75 1080w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=1200&amp;q=75 1200w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=1920&amp;q=75 1920w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=2048&amp;q=75 2048w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=3840&amp;q=75 3840w" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718529848-screen-shot-2024-06-16-at-2-24-03-am.png&amp;w=3840&amp;q=75"/></div><div font-size="textSm" font-style="italic" class="sc-6293d692-0 jgEMAk"><!--$--><!--/$--></div></div></p><h2 id="applications-of-confidence-intervals-in-machine-learning" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg">Applications of Confidence Intervals in Machine Learning</h2><p class="sc-5159831f-0">Confidence intervals provide a statistical framework that is instrumental across various facets of machine learning. Their applications range from hypothesis testing and model comparison to domain-specific implementations and enhancing the communication of machine learning results. Understanding these applications underscores the value of confidence intervals in navigating the uncertainties inherent in machine learning predictions and estimations.</p><h3 id="hypothesis-testing-within-machine-learning" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Hypothesis Testing within Machine Learning</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Assessing Model Improvements</span>: Confidence intervals are pivotal in determining whether changes in a model&#x27;s performance are statistically significant or merely due to random fluctuations in the data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Feature Importance</span>: By constructing confidence intervals around feature importance scores, machine learning practitioners can discern which features contribute meaningfully to the model&#x27;s predictions.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Example</span>: In a study examining the accuracy of different classifiers, confidence intervals enabled researchers to assert with 95% certainty which classifiers performed significantly better than others.</p></li></li></ul><h3 id="model-comparison" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Model Comparison</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Statistical Basis for Comparison</span>: Confidence intervals facilitate a rigorous statistical comparison between models, beyond mere point estimates of performance metrics.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Informed Decision-Making</span>: By quantifying the uncertainty around model performance metrics, stakeholders can make more informed choices about which model to deploy in production environments.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Case Study</span>: Research demonstrated that when comparing deep learning models to traditional machine learning models, confidence intervals around accuracy metrics provided insights into the reliability of model superiority claims.</p></li></li></ul><h3 id="domainspecific-applications" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Domain-Specific Applications</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Personalized Medicine</span>: In the realm of personalized medicine, confidence intervals help quantify the uncertainty of predictions for individual patients, thereby guiding treatment decisions with a clearer understanding of risk.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Financial Forecasting</span>: Confidence intervals are employed to assess the reliability of financial forecasts, enabling businesses to plan with a degree of certainty about future economic conditions.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Environmental Modeling</span>: Predicting climate change impacts benefits from confidence intervals by providing a range within which predicted outcomes are likely to fall, thus aiding policy formulation.</p></li></li></ul><h3 id="deep-learning" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Deep Learning</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Uncertainty in Predictions</span>: Deep learning models, known for their complexity, often yield predictions that are hard to interpret; confidence intervals introduce a measure of uncertainty into these predictions.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Improving Model Trustworthiness</span>: By quantifying the uncertainty of predictions from neural networks, machine learning engineers can evaluate the robustness of their models in a transparent manner.</p></li></li></ul><h3 id="communicating-results-to-nontechnical-stakeholders" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Communicating Results to Non-Technical Stakeholders</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Enhancing Transparency</span>: Confidence intervals offer a straightforward way to communicate the reliability of machine learning findings to stakeholders without requiring deep statistical knowledge.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Building Trust</span>: By presenting machine learning results within the framework of confidence intervals, practitioners can foster trust among users and stakeholders by openly acknowledging the limits of model predictions.</p></li></li></ul><h3 id="research-and-case-studies" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg">Research and Case Studies</h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Academic Research</span>: Studies exploring the efficacy of bootstrap confidence intervals in machine learning have shown how these intervals can adapt to the complexity of model estimations, providing accurate and robust measures of uncertainty.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Industry Applications</span>: In sectors ranging from healthcare to finance, case studies have documented the role of confidence intervals in validating the performance of predictive models, ensuring that decisions are based on statistically sound foundations.</p></li></li></ul><p class="sc-5159831f-0">The applications of confidence intervals in machine learning are as varied as they are critical. From hypothesis testing and model comparison to their role in domain-specific applications and communication of results, confidence intervals serve as a cornerstone for rigorous, transparent, and informed decision-making in the field. Their ability to quantify the uncertainty of predictions and estimations not only enhances the reliability of machine learning models but also underpins the responsible deployment of AI technologies across industries.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="OcUPVLYOTdiOH90vXDPFbA"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1512" height="788" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url(&quot;data:image/svg+xml;charset=utf-8,%3Csvg xmlns=&#x27;http://www.w3.org/2000/svg&#x27; viewBox=&#x27;0 0 1512 788&#x27;%3E%3Cfilter id=&#x27;b&#x27; color-interpolation-filters=&#x27;sRGB&#x27;%3E%3CfeGaussianBlur 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class="sc-e69ac761-0 kmKRMV">Rectified Linear Unit (ReLU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/reproducibility-machine-learning" class="sc-e69ac761-0 kmKRMV">Reproducibility in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/restricted-boltzmann-machines" class="sc-e69ac761-0 kmKRMV">Restricted Boltzmann Machines</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-supervised-learning" class="sc-e69ac761-0 kmKRMV">Semi-Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/supervised-learning" class="sc-e69ac761-0 kmKRMV">Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/support-vector-machines-svm" class="sc-e69ac761-0 kmKRMV">Support Vector Machines (SVM)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/topic-modeling" class="sc-e69ac761-0 kmKRMV">Topic Modeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/uncertainty-machine-learning" class="sc-e69ac761-0 kmKRMV">Uncertainty in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/vanishing-and-exploding-gradients" class="sc-e69ac761-0 kmKRMV">Vanishing and Exploding Gradients</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-interpretability" class="sc-e69ac761-0 kmKRMV">AI Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-labeling" class="sc-e69ac761-0 kmKRMV">Data Labeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inference-engine" class="sc-e69ac761-0 kmKRMV">Inference Engine</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/probabilistic-models-in-machine-learning" class="sc-e69ac761-0 kmKRMV">Probabilistic Models in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f1-score-machine-learning" class="sc-e69ac761-0 kmKRMV">F1 Score in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/expectation-maximization" class="sc-e69ac761-0 kmKRMV">Expectation Maximization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/beam-search-algorithm" class="sc-e69ac761-0 kmKRMV">Beam Search Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/embedding-layer" class="sc-e69ac761-0 kmKRMV">Embedding Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/differential-privacy" class="sc-e69ac761-0 kmKRMV">Differential Privacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-poisoning" class="sc-e69ac761-0 kmKRMV">Data Poisoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/causal-inference" class="sc-e69ac761-0 kmKRMV">Causal Inference</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/capsule-neural-network" class="sc-e69ac761-0 kmKRMV">Capsule Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/attention-mechanisms" class="sc-e69ac761-0 kmKRMV">Attention Mechanisms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/domain-adaptation" class="sc-e69ac761-0 kmKRMV">Domain Adaptation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/evolutionary-algorithms" class="sc-e69ac761-0 kmKRMV">Evolutionary Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/contrastive-learning" class="sc-e69ac761-0 kmKRMV">Contrastive Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/explainable-ai" class="sc-e69ac761-0 kmKRMV">Explainable AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/affective-ai" class="sc-e69ac761-0 kmKRMV">Affective AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-networks" class="sc-e69ac761-0 kmKRMV">Semantic Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-augmentation" class="sc-e69ac761-0 kmKRMV">Data Augmentation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/convolutional-neural-networks" class="sc-e69ac761-0 kmKRMV">Convolutional Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-computing" class="sc-e69ac761-0 kmKRMV">Cognitive Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/end-to-end-learning" class="sc-e69ac761-0 kmKRMV">End-to-end Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-tuning" class="sc-e69ac761-0 kmKRMV">Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/double-descent" class="sc-e69ac761-0 kmKRMV">Double Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-drift" class="sc-e69ac761-0 kmKRMV">Model Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-radiance-fields" class="sc-e69ac761-0 kmKRMV">Neural Radiance Fields</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/regularization" class="sc-e69ac761-0 kmKRMV">Regularization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-querying" class="sc-e69ac761-0 kmKRMV">Natural Language Querying (NLQ)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/foundation-models" class="sc-e69ac761-0 kmKRMV">Foundation Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/forward-propagation" class="sc-e69ac761-0 kmKRMV">Forward Propagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f2-score" class="sc-e69ac761-0 kmKRMV">F2 Score</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-ethics" class="sc-e69ac761-0 kmKRMV">AI Ethics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/transfer-learning" class="sc-e69ac761-0 kmKRMV">Transfer Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-alignment" class="sc-e69ac761-0 kmKRMV">AI Alignment</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v3" class="sc-e69ac761-0 kmKRMV">Whisper v3</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v2" class="sc-e69ac761-0 kmKRMV">Whisper v2</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-structured-data" class="sc-e69ac761-0 kmKRMV">Semi-structured data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-hallucinations" class="sc-e69ac761-0 kmKRMV">AI Hallucinations</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/emergent-behavior" class="sc-e69ac761-0 kmKRMV">Emergent Behavior</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/matplotlib" class="sc-e69ac761-0 kmKRMV">Matplotlib</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/numpy" class="sc-e69ac761-0 kmKRMV">NumPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scikit-learn" class="sc-e69ac761-0 kmKRMV">Scikit-learn</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scipy" class="sc-e69ac761-0 kmKRMV">SciPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keras" class="sc-e69ac761-0 kmKRMV">Keras</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/tensorflow" class="sc-e69ac761-0 kmKRMV">TensorFlow</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/seaborn-python-package" class="sc-e69ac761-0 kmKRMV">Seaborn Python Package</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pytorch" class="sc-e69ac761-0 kmKRMV">PyTorch</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-toolkit-nltk" class="sc-e69ac761-0 kmKRMV">Natural Language Toolkit (NLTK)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pandas" class="sc-e69ac761-0 kmKRMV">Pandas</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ego-4d" class="sc-e69ac761-0 kmKRMV">Ego 4D</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/the-pile" class="sc-e69ac761-0 kmKRMV">The Pile</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/common-crawl-datasets" class="sc-e69ac761-0 kmKRMV">Common Crawl Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/squad" class="sc-e69ac761-0 kmKRMV">SQuAD</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/intelligent-document-processing" class="sc-e69ac761-0 kmKRMV">Intelligent Document Processing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameter-tuning" class="sc-e69ac761-0 kmKRMV">Hyperparameter Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/Markov-decision-process" class="sc-e69ac761-0 kmKRMV">Markov Decision Process</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graph-neural-networks" class="sc-e69ac761-0 kmKRMV">Graph Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-architecture-search" class="sc-e69ac761-0 kmKRMV">Neural Architecture Search</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ablation" class="sc-e69ac761-0 kmKRMV">Ablation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-distillation" class="sc-e69ac761-0 kmKRMV">Knowledge Distillation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-interpretability" class="sc-e69ac761-0 kmKRMV">Model Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/out-of-distribution-detection" class="sc-e69ac761-0 kmKRMV">Out-of-Distribution Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/recurrent-neural-networks" class="sc-e69ac761-0 kmKRMV">Recurrent Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/active-learning" class="sc-e69ac761-0 kmKRMV">Active Learning (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imbalanced-data" class="sc-e69ac761-0 kmKRMV">Imbalanced Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/loss-function" class="sc-e69ac761-0 kmKRMV">Loss Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/unsupervised-learning" class="sc-e69ac761-0 kmKRMV">Unsupervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-and-big-data" class="sc-e69ac761-0 kmKRMV">AI and Big Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/adagrad" class="sc-e69ac761-0 kmKRMV">AdaGrad</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering-algorithms" class="sc-e69ac761-0 kmKRMV">Clustering Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/parametric-neural-networks%C2%A0" class="sc-e69ac761-0 kmKRMV">Parametric Neural Networks </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/acoustic-models" class="sc-e69ac761-0 kmKRMV">Acoustic Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/articulatory-synthesis" class="sc-e69ac761-0 kmKRMV">Articulatory Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/concatenative-synthesis" class="sc-e69ac761-0 kmKRMV">Concatenative Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grapheme-to-phoneme-conversion-g2p" class="sc-e69ac761-0 kmKRMV">Grapheme-to-Phoneme Conversion (G2P)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/homograph-disambiguation" class="sc-e69ac761-0 kmKRMV">Homograph Disambiguation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-text-to-speech-ntts" class="sc-e69ac761-0 kmKRMV">Neural Text-to-Speech (NTTS)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/voice-cloning" class="sc-e69ac761-0 kmKRMV">Voice Cloning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/autoregressive-model" class="sc-e69ac761-0 kmKRMV">Autoregressive Model</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/candidate-sampling" class="sc-e69ac761-0 kmKRMV">Candidate Sampling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-algorithmic-trading" class="sc-e69ac761-0 kmKRMV">Machine Learning in Algorithmic Trading</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-creativity" class="sc-e69ac761-0 kmKRMV">Computational Creativity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/context-aware-computing" class="sc-e69ac761-0 kmKRMV">Context-Aware Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-emotion-recognition" class="sc-e69ac761-0 kmKRMV">AI Emotion Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-representation-and-reasoning" class="sc-e69ac761-0 kmKRMV">Knowledge Representation and Reasoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metacognitive-learning-models" class="sc-e69ac761-0 kmKRMV">Metacognitive Learning Models </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/synthetic-data-for-ai-training" class="sc-e69ac761-0 kmKRMV">Synthetic Data for AI Training</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-speech-enhancement" class="sc-e69ac761-0 kmKRMV">AI Speech Enhancement</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/counterfactual-explanations-in-ai" class="sc-e69ac761-0 kmKRMV">Counterfactual Explanations in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/eco-friendly-ai" class="sc-e69ac761-0 kmKRMV">Eco-friendly AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-store-for-machine-learning" class="sc-e69ac761-0 kmKRMV">Feature Store for Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-teaching-networks" class="sc-e69ac761-0 kmKRMV">Generative Teaching Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-centered-ai" class="sc-e69ac761-0 kmKRMV">Human-centered AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metaheuristic-algorithms" class="sc-e69ac761-0 kmKRMV">Metaheuristic Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/statistical-relational-learning" class="sc-e69ac761-0 kmKRMV">Statistical Relational Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-architectures" class="sc-e69ac761-0 kmKRMV">Cognitive Architectures</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-phenotyping" class="sc-e69ac761-0 kmKRMV">Computational Phenotyping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/continuous-learning-systems" class="sc-e69ac761-0 kmKRMV">Continuous Learning Systems</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deepfake-detection" class="sc-e69ac761-0 kmKRMV">Deepfake Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/one-shot-learning" class="sc-e69ac761-0 kmKRMV">One-Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/quantum-machine-learning-algorithms" class="sc-e69ac761-0 kmKRMV">Quantum Machine Learning Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/self-healing-ai" class="sc-e69ac761-0 kmKRMV">Self-healing AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-search-algorithms" class="sc-e69ac761-0 kmKRMV">Semantic Search Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/artificial-super-intelligence" class="sc-e69ac761-0 kmKRMV">Artificial Super Intelligence</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-guardrails" class="sc-e69ac761-0 kmKRMV">AI Guardrails</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/limited-memory-ai" class="sc-e69ac761-0 kmKRMV">Limited Memory AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatbots" class="sc-e69ac761-0 kmKRMV">Chatbots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion" class="sc-e69ac761-0 kmKRMV">Diffusion</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-layer" class="sc-e69ac761-0 kmKRMV">Hidden Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/instruction-tuning" class="sc-e69ac761-0 kmKRMV">Instruction Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/objective-function" class="sc-e69ac761-0 kmKRMV">Objective Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pretraining" class="sc-e69ac761-0 kmKRMV">Pretraining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/symbolic-ai" class="sc-e69ac761-0 kmKRMV">Symbolic AI</a><a rel="" target="" font-size="textLg" font-weight="medium" 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary sc-d74559df-0 iotBFW css-ak4akz" tabindex="0" type="button" href="" target="_self"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex">B</span></button></li><li class="sc-ace17a57-0 goWpow"><style data-emotion="css q0kznr">.css-q0kznr{font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary sc-d74559df-0 dTOZsF css-ak4akz" tabindex="0" type="button" href="" target="_self"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex">C</span></button></li><li class="sc-ace17a57-0 goWpow"><style data-emotion="css q0kznr">.css-q0kznr{font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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href="/ai-glossary/ai-and-education" class="sc-e69ac761-0 dsCZKx">AI and Education</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-and-medicine" class="sc-e69ac761-0 dsCZKx">AI and Medicine</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-voice-transfer" class="sc-e69ac761-0 dsCZKx">AI Voice Transfer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/approximate-dynamic-programming" class="sc-e69ac761-0 dsCZKx">Approximate Dynamic Programming</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/adversarial-machine-learning" class="sc-e69ac761-0 dsCZKx">Adversarial Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/alphago-zero" class="sc-e69ac761-0 dsCZKx">AlphaGo Zero</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-hardware" class="sc-e69ac761-0 dsCZKx">AI Hardware</a><a 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class="sc-e69ac761-0 dsCZKx">AI Lifecycle Management</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-literacy" class="sc-e69ac761-0 dsCZKx">AI Literacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-monitoring" class="sc-e69ac761-0 dsCZKx">AI Monitoring</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-oversight" class="sc-e69ac761-0 dsCZKx">AI Oversight</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-privacy" class="sc-e69ac761-0 dsCZKx">AI Privacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-prototyping" class="sc-e69ac761-0 dsCZKx">AI Prototyping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-regulation" class="sc-e69ac761-0 dsCZKx">AI Regulation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-resilience" class="sc-e69ac761-0 dsCZKx">AI Resilience</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-interpretability" class="sc-e69ac761-0 dsCZKx">AI Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/attention-mechanisms" class="sc-e69ac761-0 dsCZKx">Attention Mechanisms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/affective-ai" class="sc-e69ac761-0 dsCZKx">Affective AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-ethics" class="sc-e69ac761-0 dsCZKx">AI Ethics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-alignment" class="sc-e69ac761-0 dsCZKx">AI Alignment</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-hallucinations" class="sc-e69ac761-0 dsCZKx">AI Hallucinations</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ablation" class="sc-e69ac761-0 dsCZKx">Ablation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/active-learning" class="sc-e69ac761-0 dsCZKx">Active Learning (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-and-big-data" class="sc-e69ac761-0 dsCZKx">AI and Big Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/adagrad" class="sc-e69ac761-0 dsCZKx">AdaGrad</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/acoustic-models" class="sc-e69ac761-0 dsCZKx">Acoustic Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/articulatory-synthesis" class="sc-e69ac761-0 dsCZKx">Articulatory Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/autoregressive-model" class="sc-e69ac761-0 dsCZKx">Autoregressive Model</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-emotion-recognition" class="sc-e69ac761-0 dsCZKx">AI Emotion Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-speech-enhancement" class="sc-e69ac761-0 dsCZKx">AI Speech Enhancement</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/artificial-super-intelligence" class="sc-e69ac761-0 dsCZKx">Artificial Super Intelligence</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-guardrails" class="sc-e69ac761-0 dsCZKx">AI Guardrails</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/auto-classification" class="sc-e69ac761-0 dsCZKx">Auto Classification</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/association-rule-learning" class="sc-e69ac761-0 dsCZKx">Association Rule Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/autoencoder" class="sc-e69ac761-0 dsCZKx">Autoencoder</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/accuracy" class="sc-e69ac761-0 dsCZKx">Accuracy in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-detection" class="sc-e69ac761-0 dsCZKx">AI Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-robustness" class="sc-e69ac761-0 dsCZKx">AI Robustness</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-safety" class="sc-e69ac761-0 dsCZKx">AI Safety</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-scalability" class="sc-e69ac761-0 dsCZKx">AI Scalability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-simulation" class="sc-e69ac761-0 dsCZKx">AI Simulation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-standards" class="sc-e69ac761-0 dsCZKx">AI Standards</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-steering" class="sc-e69ac761-0 dsCZKx">AI Steering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-transparency" class="sc-e69ac761-0 dsCZKx">AI Transparency</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/augmented-intelligence" class="sc-e69ac761-0 dsCZKx">Augmented Intelligence</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/applications" class="sc-e69ac761-0 dsCZKx">Applications</a></li><li data-letter="B" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">B</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/benchmarking" class="sc-e69ac761-0 dsCZKx">Benchmarking</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/batch-gradient-descent" class="sc-e69ac761-0 dsCZKx">Batch Gradient Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/backpropagation" class="sc-e69ac761-0 dsCZKx">Backpropagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bayesian-machine-learning" class="sc-e69ac761-0 dsCZKx">Bayesian Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bert" class="sc-e69ac761-0 dsCZKx">BERT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/binary-classification-ai" class="sc-e69ac761-0 dsCZKx">Binary Classification AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/beam-search-algorithm" class="sc-e69ac761-0 dsCZKx">Beam Search Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bias-variance-tradeoff" class="sc-e69ac761-0 dsCZKx">Bias-Variance Tradeoff</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/boosting" class="sc-e69ac761-0 dsCZKx">Boosting in Machine Learning</a></li><li data-letter="C" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 fvIpti">C</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chess-bots" class="sc-e69ac761-0 dsCZKx">Chess bots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatgpt" class="sc-e69ac761-0 dsCZKx">ChatGPT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cure-algorithm" class="sc-e69ac761-0 dsCZKx">CURE Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/curse-of-dimensionality" class="sc-e69ac761-0 dsCZKx">Curse of Dimensionality</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/classification" class="sc-e69ac761-0 dsCZKx">Classification</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-map" class="sc-e69ac761-0 dsCZKx">Cognitive Map</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/central-processing-unit-cpu" class="sc-e69ac761-0 dsCZKx">Central Processing Unit (CPU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/conditional-variational-autoencoders" class="sc-e69ac761-0 dsCZKx">Conditional Variational Autoencoders</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/conversational-ai" class="sc-e69ac761-0 dsCZKx">Conversational AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/causal-inference" class="sc-e69ac761-0 dsCZKx">Causal Inference</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/capsule-neural-network" class="sc-e69ac761-0 dsCZKx">Capsule Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/contrastive-learning" class="sc-e69ac761-0 dsCZKx">Contrastive Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/convolutional-neural-networks" class="sc-e69ac761-0 dsCZKx">Convolutional Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-computing" class="sc-e69ac761-0 dsCZKx">Cognitive Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/common-crawl-datasets" class="sc-e69ac761-0 dsCZKx">Common Crawl Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering-algorithms" class="sc-e69ac761-0 dsCZKx">Clustering Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/concatenative-synthesis" class="sc-e69ac761-0 dsCZKx">Concatenative Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/candidate-sampling" class="sc-e69ac761-0 dsCZKx">Candidate Sampling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-creativity" class="sc-e69ac761-0 dsCZKx">Computational Creativity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/context-aware-computing" class="sc-e69ac761-0 dsCZKx">Context-Aware Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/counterfactual-explanations-in-ai" class="sc-e69ac761-0 dsCZKx">Counterfactual Explanations in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-architectures" class="sc-e69ac761-0 dsCZKx">Cognitive Architectures</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-phenotyping" class="sc-e69ac761-0 dsCZKx">Computational Phenotyping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/continuous-learning-systems" class="sc-e69ac761-0 dsCZKx">Continuous Learning Systems</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatbots" class="sc-e69ac761-0 dsCZKx">Chatbots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/composite-ai" class="sc-e69ac761-0 dsCZKx">Composite AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-lingustics" class="sc-e69ac761-0 dsCZKx">Computational Linguistics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-semantics" class="sc-e69ac761-0 dsCZKx">Computational Semantics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/collaborative-filtering" class="sc-e69ac761-0 dsCZKx">Collaborative Filtering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/corpus" class="sc-e69ac761-0 dsCZKx">Corpus in NLP</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/confirmation-bias" class="sc-e69ac761-0 dsCZKx">Confirmation Bias in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/confidence-intervals" class="sc-e69ac761-0 ezFGlW">Confidence Intervals in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cross-validation" class="sc-e69ac761-0 dsCZKx">Cross Validation in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering" class="sc-e69ac761-0 dsCZKx">Clustering in Machine Learning</a></li><li data-letter="D" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">D</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/dall-e" class="sc-e69ac761-0 dsCZKx">Dall-E</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/distilbert" class="sc-e69ac761-0 dsCZKx">DistilBERT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/dimensionality-reduction" class="sc-e69ac761-0 dsCZKx">Dimensionality Reduction</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deep-reinforcement-learning" class="sc-e69ac761-0 dsCZKx">Deep Reinforcement Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion-model" class="sc-e69ac761-0 dsCZKx">Diffusion Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deep-learning" class="sc-e69ac761-0 dsCZKx">Deep Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/datasets" class="sc-e69ac761-0 dsCZKx">Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-labeling" class="sc-e69ac761-0 dsCZKx">Data Labeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/differential-privacy" class="sc-e69ac761-0 dsCZKx">Differential Privacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-poisoning" class="sc-e69ac761-0 dsCZKx">Data Poisoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/domain-adaptation" class="sc-e69ac761-0 dsCZKx">Domain Adaptation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-augmentation" class="sc-e69ac761-0 dsCZKx">Data Augmentation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/double-descent" class="sc-e69ac761-0 dsCZKx">Double Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deepfake-detection" class="sc-e69ac761-0 dsCZKx">Deepfake Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion" class="sc-e69ac761-0 dsCZKx">Diffusion</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-drift" class="sc-e69ac761-0 dsCZKx">Data Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-scarcity" class="sc-e69ac761-0 dsCZKx">Data Scarcity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/decision-tree" class="sc-e69ac761-0 dsCZKx">Decision Tree</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/decision-intelligence" class="sc-e69ac761-0 dsCZKx">Decision Intelligence</a></li><li data-letter="E" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">E</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/expectation-maximization" class="sc-e69ac761-0 dsCZKx">Expectation Maximization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/embedding-layer" class="sc-e69ac761-0 dsCZKx">Embedding Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/evolutionary-algorithms" class="sc-e69ac761-0 dsCZKx">Evolutionary Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/explainable-ai" class="sc-e69ac761-0 dsCZKx">Explainable AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/end-to-end-learning" class="sc-e69ac761-0 dsCZKx">End-to-end Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/emergent-behavior" class="sc-e69ac761-0 dsCZKx">Emergent Behavior</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ego-4d" class="sc-e69ac761-0 dsCZKx">Ego 4D</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/eco-friendly-ai" class="sc-e69ac761-0 dsCZKx">Eco-friendly AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ensemble-learning" class="sc-e69ac761-0 dsCZKx">Ensemble Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/entropy" class="sc-e69ac761-0 dsCZKx">Entropy in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/epoch" class="sc-e69ac761-0 dsCZKx">Epoch in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ethical-ai" class="sc-e69ac761-0 dsCZKx">Ethical AI</a></li><li data-letter="F" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">F</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/flajolet-martin-algorithm" class="sc-e69ac761-0 dsCZKx">Flajolet-Martin Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feedforward-neural-network" class="sc-e69ac761-0 dsCZKx">Feedforward Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/fine-tuning-deep-learning" class="sc-e69ac761-0 dsCZKx">Fine Tuning in Deep Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/fundamentals" class="sc-e69ac761-0 dsCZKx">Fundamentals</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f1-score-machine-learning" class="sc-e69ac761-0 dsCZKx">F1 Score in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/foundation-models" class="sc-e69ac761-0 dsCZKx">Foundation Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/forward-propagation" class="sc-e69ac761-0 dsCZKx">Forward Propagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f2-score" class="sc-e69ac761-0 dsCZKx">F2 Score</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-store-for-machine-learning" class="sc-e69ac761-0 dsCZKx">Feature Store for Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/few-shot-learning" class="sc-e69ac761-0 dsCZKx">Few Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/federated-learning" class="sc-e69ac761-0 dsCZKx">Federated Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-learning" class="sc-e69ac761-0 dsCZKx">Feature Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-selection" class="sc-e69ac761-0 dsCZKx">Feature Selection</a></li><li data-letter="G" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">G</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-clipping" class="sc-e69ac761-0 dsCZKx">Gradient Clipping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-adversarial-networks" class="sc-e69ac761-0 dsCZKx">Generative Adversarial Networks (GANs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gaussian-processes" class="sc-e69ac761-0 dsCZKx">Gaussian Processes</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gated-recurrent-unit" class="sc-e69ac761-0 dsCZKx">Gated Recurrent Unit</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grounding" class="sc-e69ac761-0 dsCZKx">Grounding</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-boosting-machines" class="sc-e69ac761-0 dsCZKx">Gradient Boosting Machines (GBMs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graphics-processing-unit-gpu" class="sc-e69ac761-0 dsCZKx">Graphics Processing Unit (GPU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/google-bard" class="sc-e69ac761-0 dsCZKx">Google&#x27;s Bard</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-scaling" class="sc-e69ac761-0 dsCZKx">Gradient Scaling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-ai" class="sc-e69ac761-0 dsCZKx">Generative AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graph-neural-networks" class="sc-e69ac761-0 dsCZKx">Graph Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grapheme-to-phoneme-conversion-g2p" class="sc-e69ac761-0 dsCZKx">Grapheme-to-Phoneme Conversion (G2P)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-teaching-networks" class="sc-e69ac761-0 dsCZKx">Generative Teaching Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/genetic-algorithms" class="sc-e69ac761-0 dsCZKx">Genetic Algorithms in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ground-truth" class="sc-e69ac761-0 dsCZKx">Ground Truth in Machine Learning</a></li><li data-letter="H" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">H</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameters" class="sc-e69ac761-0 dsCZKx">Hyperparameters</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-markov-models" class="sc-e69ac761-0 dsCZKx">Hidden Markov Models (HMMs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hooke-jeeves-algorithm" class="sc-e69ac761-0 dsCZKx">Hooke-Jeeves Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameter-tuning" class="sc-e69ac761-0 dsCZKx">Hyperparameter Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/homograph-disambiguation" class="sc-e69ac761-0 dsCZKx">Homograph Disambiguation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-centered-ai" class="sc-e69ac761-0 dsCZKx">Human-centered AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-layer" class="sc-e69ac761-0 dsCZKx">Hidden Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-in-the-loop-ai" class="sc-e69ac761-0 dsCZKx">Human-in-the-Loop AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hybrid-ai" class="sc-e69ac761-0 dsCZKx">Hybrid AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-augmentation-with-ai" class="sc-e69ac761-0 dsCZKx">Human Augmentation with AI</a></li><li data-letter="I" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">I</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inference-engine" class="sc-e69ac761-0 dsCZKx">Inference Engine</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/intelligent-document-processing" class="sc-e69ac761-0 dsCZKx">Intelligent Document Processing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imbalanced-data" class="sc-e69ac761-0 dsCZKx">Imbalanced Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/instruction-tuning" class="sc-e69ac761-0 dsCZKx">Instruction Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/incremental-learning" class="sc-e69ac761-0 dsCZKx">Incremental Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/information-retrieval" class="sc-e69ac761-0 dsCZKx">Information Retrieval</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/image-recognition" class="sc-e69ac761-0 dsCZKx">Image Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imagenet" class="sc-e69ac761-0 dsCZKx">ImageNet</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inductive-bias" class="sc-e69ac761-0 dsCZKx">Inductive Bias</a></li><li data-letter="K" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">K</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/k-shingles" class="sc-e69ac761-0 dsCZKx">k-Shingles</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keyphrase-extraction" class="sc-e69ac761-0 dsCZKx">Keyphrase Extraction</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keras" class="sc-e69ac761-0 dsCZKx">Keras</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-distillation" class="sc-e69ac761-0 dsCZKx">Knowledge Distillation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-representation-and-reasoning" class="sc-e69ac761-0 dsCZKx">Knowledge Representation and Reasoning</a></li><li data-letter="L" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">L</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/llama-2" class="sc-e69ac761-0 dsCZKx">Llama 2</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/llm-collection" class="sc-e69ac761-0 dsCZKx">LLM Collection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/latent-dirichlet-allocation" class="sc-e69ac761-0 dsCZKx">Latent Dirichlet Allocation (LDA)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/large-language-model" class="sc-e69ac761-0 dsCZKx">Large Language Model (LLM)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/loss-function" class="sc-e69ac761-0 dsCZKx">Loss Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/limited-memory-ai" class="sc-e69ac761-0 dsCZKx">Limited Memory AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/learning-rate" class="sc-e69ac761-0 dsCZKx">Learning Rate</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/learning-to-rank" class="sc-e69ac761-0 dsCZKx">Learning To Rank</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/logits" class="sc-e69ac761-0 dsCZKx">Logits</a></li><li data-letter="M" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">M</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/midjourney-image-generation" class="sc-e69ac761-0 dsCZKx">Midjourney (Image Generation)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mistral" class="sc-e69ac761-0 dsCZKx">Mistral</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mixture-of-experts" class="sc-e69ac761-0 dsCZKx">Mixture of Experts</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-ai" class="sc-e69ac761-0 dsCZKx">Multimodal AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-learning" class="sc-e69ac761-0 dsCZKx">Multimodal Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning" class="sc-e69ac761-0 dsCZKx">Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-aI-models-and-modalities" class="sc-e69ac761-0 dsCZKx">Multimodal AI Models and Modalities</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mamba" class="sc-e69ac761-0 dsCZKx">Mamba</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/models" class="sc-e69ac761-0 dsCZKx">Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-bias" class="sc-e69ac761-0 dsCZKx">Machine Learning Bias</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-life-cycle-management" class="sc-e69ac761-0 dsCZKx">Machine Learning Life Cycle Management</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-translation" class="sc-e69ac761-0 dsCZKx">Machine Translation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mlops" class="sc-e69ac761-0 dsCZKx">MLOps</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/monte-carlo-learning" class="sc-e69ac761-0 dsCZKx">Monte Carlo Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multi-task-learning" class="sc-e69ac761-0 dsCZKx">Multi-task Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-neuron" class="sc-e69ac761-0 dsCZKx">Machine Learning Neuron</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-preprocessing" class="sc-e69ac761-0 dsCZKx">Machine Learning Preprocessing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-drift" class="sc-e69ac761-0 dsCZKx">Model Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/matplotlib" class="sc-e69ac761-0 dsCZKx">Matplotlib</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/Markov-decision-process" class="sc-e69ac761-0 dsCZKx">Markov Decision Process</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-interpretability" class="sc-e69ac761-0 dsCZKx">Model Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-algorithmic-trading" class="sc-e69ac761-0 dsCZKx">Machine Learning in Algorithmic Trading</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metacognitive-learning-models" class="sc-e69ac761-0 dsCZKx">Metacognitive Learning Models </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metaheuristic-algorithms" class="sc-e69ac761-0 dsCZKx">Metaheuristic Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multitask-prompt-tuning" class="sc-e69ac761-0 dsCZKx">Multitask Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multi-agent-systems" class="sc-e69ac761-0 dsCZKx">Multi-Agent Systems</a></li><li data-letter="N" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">N</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-processing" class="sc-e69ac761-0 dsCZKx">Natural Language Processing (NLP)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-generation" class="sc-e69ac761-0 dsCZKx">Natural Language Generation (NLG)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-understanding" class="sc-e69ac761-0 dsCZKx">Natural Language Understanding (NLU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neuralink" class="sc-e69ac761-0 dsCZKx">Neuralink</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/naive-bayes-classifier" class="sc-e69ac761-0 dsCZKx">Naive Bayes Classifier</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-radiance-fields" class="sc-e69ac761-0 dsCZKx">Neural Radiance Fields</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-querying" class="sc-e69ac761-0 dsCZKx">Natural Language Querying (NLQ)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/numpy" class="sc-e69ac761-0 dsCZKx">NumPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-toolkit-nltk" class="sc-e69ac761-0 dsCZKx">Natural Language Toolkit (NLTK)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-architecture-search" class="sc-e69ac761-0 dsCZKx">Neural Architecture Search</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-text-to-speech-ntts" class="sc-e69ac761-0 dsCZKx">Neural Text-to-Speech (NTTS)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/named-entity-recognition" class="sc-e69ac761-0 dsCZKx">Named Entity Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-style-transfer" class="sc-e69ac761-0 dsCZKx">Neural Style Transfer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neuroevolution" class="sc-e69ac761-0 dsCZKx">Neuroevolution</a></li><li data-letter="O" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">O</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/online-gradient-descent" class="sc-e69ac761-0 dsCZKx">Online Gradient Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/overfitting-underfitting" class="sc-e69ac761-0 dsCZKx">Overfitting and Underfitting</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/openai-whisper" class="sc-e69ac761-0 dsCZKx">OpenAI Whisper</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/openai-sora" class="sc-e69ac761-0 dsCZKx">OpenAI Sora</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/out-of-distribution-detection" class="sc-e69ac761-0 dsCZKx">Out-of-Distribution Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/one-shot-learning" class="sc-e69ac761-0 dsCZKx">One-Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/objective-function" class="sc-e69ac761-0 dsCZKx">Objective Function</a></li><li data-letter="P" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">P</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-engineering" class="sc-e69ac761-0 dsCZKx">Prompt Engineering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-chaining" class="sc-e69ac761-0 dsCZKx">Prompt Chaining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/perceptron" class="sc-e69ac761-0 dsCZKx">Perceptron</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/precision-and-recall" class="sc-e69ac761-0 dsCZKx">Precision and Recall</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/packages-glossary" class="sc-e69ac761-0 dsCZKx">Packages</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pooling-machine-learning" class="sc-e69ac761-0 dsCZKx">Pooling (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/principal-component-analysis" class="sc-e69ac761-0 dsCZKx">Principal Component Analysis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/probabilistic-models-in-machine-learning" class="sc-e69ac761-0 dsCZKx">Probabilistic Models in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-tuning" class="sc-e69ac761-0 dsCZKx">Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pytorch" class="sc-e69ac761-0 dsCZKx">PyTorch</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pandas" class="sc-e69ac761-0 dsCZKx">Pandas</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/parametric-neural-networks%C2%A0" class="sc-e69ac761-0 dsCZKx">Parametric Neural Networks </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pretraining" class="sc-e69ac761-0 dsCZKx">Pretraining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/part-of-speech-tagging" class="sc-e69ac761-0 dsCZKx">Part-of-Speech Tagging</a></li><li data-letter="Q" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">Q</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/quantum-machine-learning-algorithms" class="sc-e69ac761-0 dsCZKx">Quantum Machine Learning Algorithms</a></li><li data-letter="R" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" 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Deepgram</span></div></div></div></footer></div></div><script id="__NEXT_DATA__" type="application/json">{"props":{"pageProps":{"slug":["confidence-intervals"],"pageData":{"templateGlossary":{"__typename":"TemplateGlossaryRecord","id":"HN35MvNlTrmltLsdT_zpXA","seo":null,"slug":"confidence-intervals","title":"Confidence Intervals in Machine Learning","categoryPage":false,"excerpt":{"__typename":"TemplateGlossaryModelExcerptField","value":{"schema":"dast","document":{"type":"root","children":[{"type":"paragraph","children":[{"type":"span","value":"This article delves deep into the world of confidence intervals within the machine learning landscape. "}]}]}}},"body":{"__typename":"TemplateGlossaryModelBodyField","blocks":[],"links":[{"__typename":"ComponentImageRecord","id":"Z5su9I_yQ16q7vzUlugSsg","caption":"Ever wanted to learn how to build an LLM Chatbot from scratch? Check out [this article](https://deepgram.com/learn/building-an-end-to-end-llm-chatbot) to learn how!","imageDesktop":{"__typename":"FileField","id":"aAdLHPi7SYKaLLoWjBaYpg","title":null,"filename":"screen-shot-2024-06-16-at-2-09-13-am.png","size":1528630,"alt":null,"url":"https://www.datocms-assets.com/96965/1718528956-screen-shot-2024-06-16-at-2-09-13-am.png","width":1472,"height":950},"imageMobile":null,"link":""},{"__typename":"ComponentImageRecord","id":"IbSwv5QJQCyBYp86KUZZnA","caption":"AI emits Carbon, but how much do we get in return? [This article](https://deepgram.com/learn/ai-carbon-cost) examines the environmental cost of AI and exactly what benefits may be reaped.","imageDesktop":{"__typename":"FileField","id":"GvMOgM7RQ7eLGfAH9wOOdg","title":null,"filename":"screen-shot-2024-06-16-at-2-12-39-am.png","size":2257055,"alt":null,"url":"https://www.datocms-assets.com/96965/1718529161-screen-shot-2024-06-16-at-2-12-39-am.png","width":1502,"height":886},"imageMobile":null,"link":""},{"__typename":"ComponentImageRecord","id":"FaceuzhAQRGLZjVVvAu5fQ","caption":"Do you know how to spot a deepfake? Or how to tell when a voice has been cloned? Learn expert detection techniques in [this article](https://deepgram.com/learn/navigating-deepfakes-and-voice-cloning-how-to-safeguard).","imageDesktop":{"__typename":"FileField","id":"GhXp3bFtQVWXayQ7ClZT5A","title":null,"filename":"screen-shot-2024-06-16-at-2-24-03-am.png","size":2022310,"alt":null,"url":"https://www.datocms-assets.com/96965/1718529848-screen-shot-2024-06-16-at-2-24-03-am.png","width":1492,"height":960},"imageMobile":null,"link":""},{"__typename":"ComponentImageRecord","id":"OcUPVLYOTdiOH90vXDPFbA","caption":"Mixture of Experts (MoE) is a method that presents an efficient approach to dramatically increasing a model’s capabilities without introducing a proportional amount of computational overhead. To learn more, check out [this guide](https://deepgram.com/learn/mixture-of-experts-ml-model-guide)!","imageDesktop":{"__typename":"FileField","id":"cnmz5FWiQv2S--QFhqNL-g","title":null,"filename":"screen-shot-2024-06-16-at-2-06-22-am.png","size":2233720,"alt":null,"url":"https://www.datocms-assets.com/96965/1718528786-screen-shot-2024-06-16-at-2-06-22-am.png","width":1512,"height":788},"imageMobile":null,"link":""}],"value":{"schema":"dast","document":{"type":"root","children":[{"type":"paragraph","children":[{"type":"span","value":"Have you ever wondered how machine learning models make predictions with such precision, yet we're advised to take these predictions with a grain of uncertainty? In the realm of machine learning, confidence intervals emerge as a beacon of reliability, guiding practitioners through the fog of predictive analytics. A staggering fact: despite the rapid advancements in machine learning methodologies, the interpretation of model outputs often remains a daunting challenge for many. Understanding confidence intervals in machine learning not only demystifies this aspect but also empowers users to gauge the reliability and stability of their models effectively."}]},{"type":"paragraph","children":[{"type":"span","value":"This article delves deep into the world of confidence intervals within the machine learning landscape. You'll gain a foundational understanding of what confidence intervals are and why they're paramount for quantifying the uncertainty of predictions or parameter estimations in machine learning models. From the practical insights shared by Sebastian Raschka to the critical importance of these intervals in evaluating model performance, this piece covers it all. Expect to uncover how confidence intervals provide a statistical basis for making informed decisions, especially when it comes to interpreting the performance of machine learning models in real-world scenarios."}]},{"type":"paragraph","children":[{"type":"span","value":"Are you ready to navigate through the intricacies of confidence intervals and unlock new levels of confidence in your machine learning endeavors? Let's explore how these statistical techniques not only quantify uncertainty but also illuminate the path to more reliable and generalizable machine learning models."}]},{"type":"heading","level":2,"children":[{"type":"span","value":"What are confidence intervals in machine learning"}]},{"type":"paragraph","children":[{"type":"span","value":"In the vast expanse of machine learning, confidence intervals stand out as statistical techniques crucial for determining the reliability of an estimate. But what exactly are confidence intervals, and how do they apply to machine learning? Let's break it down:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Confidence intervals"},{"type":"span","value":" provide a range within which we expect the true value of a parameter to lie, with a certain level of confidence, typically 95%. This means that if we were to repeat our study multiple times, 95% of the confidence intervals calculated from those studies would contain the true parameter value."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"They play a pivotal role in "},{"type":"span","marks":["strong"],"value":"quantifying the uncertainty"},{"type":"span","value":" of a prediction or parameter estimation in machine learning models. This quantification is vital for practitioners to assess the stability and reliability of their models."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"A practical explanation on creating confidence intervals around an estimated value in classifiers can be found in "},{"type":"span","marks":["strong"],"value":"Sebastian Raschka's blog"},{"type":"span","value":". Raschka's insights shed light on the methodology and importance of incorporating confidence intervals in machine learning workflows."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Understanding confidence intervals"},{"type":"span","value":" is essential for evaluating the generalizability of a machine learning model to new, unseen data. This insight is invaluable, especially in scenarios where decisions are based on predictions or estimations derived from machine learning models."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"The significance of confidence intervals extends beyond mere statistical measures; they offer insights into the stability and reliability of machine learning models. This enables practitioners to make informed decisions and interpretations regarding the performance of their models."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"In essence, confidence intervals serve as a critical tool in the arsenal of machine learning practitioners, providing a statistical foundation to the often uncertain task of model prediction and parameter estimation."}]},{"type":"paragraph","children":[{"item":"Z5su9I_yQ16q7vzUlugSsg","type":"inlineItem"}]},{"type":"heading","level":2,"children":[{"type":"span","value":"Calculating Confidence Intervals in Machine Learning"}]},{"type":"paragraph","children":[{"type":"span","value":"The calculation of confidence intervals in machine learning is a nuanced process that blends statistical theory with computational techniques. This section explores the methodologies and mathematical foundations that underpin the calculation of confidence intervals, offering insights into their practical application in machine learning scenarios."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"General Formula for Calculating Confidence Intervals"}]},{"type":"paragraph","children":[{"type":"span","value":"The cornerstone of calculating confidence intervals involves a few key components:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Estimated Parameter"},{"type":"span","value":": This could be any statistic, such as the mean or median, derived from your dataset."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Critical Value"},{"type":"span","value":": Depending on the confidence level chosen, this value (z-score or t-score) quantifies the degree to which the estimated parameter can vary from the true population parameter."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Standard Error of the Estimate"},{"type":"span","value":": This measures the dispersion of the sample mean from the population mean."}]}]}]},{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"The Formula"},{"type":"span","value":": Confidence Interval = Estimated Parameter ± (Critical Value * Standard Error)"}]},{"type":"paragraph","children":[{"type":"span","value":"This formula underpins the creation of confidence intervals across various statistical and machine learning applications, serving as a fundamental tool for quantifying uncertainty."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Bootstrap Method for Confidence Intervals"}]},{"type":"paragraph","children":[{"type":"span","value":"The bootstrap method, as elaborated on GeeksforGeeks, offers a powerful, non-parametric approach to estimating confidence intervals:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Resampling"},{"type":"span","value":": This involves randomly selecting observations from the dataset, with replacement, to create multiple samples."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Estimation"},{"type":"span","value":": For each resampled dataset, calculate the statistic of interest."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Confidence Interval Calculation"},{"type":"span","value":": Determine the distribution of the estimated statistics and then calculate the desired confidence interval."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"This method is particularly useful in situations where the theoretical distribution of the statistic is unknown or difficult to determine."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Cross-Validation Techniques for Model Stability"}]},{"type":"paragraph","children":[{"type":"span","value":"Cross-validation plays a crucial role in assessing model stability and calculating confidence intervals for model accuracy. Insights from Junjie Zhang's 2019 research highlight how cross-validation can be instrumental:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Model Evaluation"},{"type":"span","value":": By partitioning the dataset into training and testing sets, cross-validation allows for the evaluation of model performance across multiple subsets of data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Confidence Interval Estimation"},{"type":"span","value":": Through repeated sampling and testing, confidence intervals for model accuracy can be derived, offering insights into the model's generalizability and stability."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Prediction Intervals vs. Confidence Intervals"}]},{"type":"paragraph","children":[{"type":"span","value":"While closely related, prediction intervals and confidence intervals cater to different aspects of uncertainty:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Prediction Intervals"},{"type":"span","value":": Focus on the uncertainty surrounding individual predictions made by the model."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Confidence Intervals"},{"type":"span","value":": Aim to quantify the uncertainty around an estimated parameter of the population from which the dataset was sampled."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Understanding the distinction between these two concepts is crucial for accurate interpretation of model outputs."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Utilizing Statistical Software and Programming Languages"}]},{"type":"paragraph","children":[{"type":"span","value":"Python emerges as a leading tool for calculating confidence intervals, with various libraries and online resources enhancing its capability:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Statistical Libraries"},{"type":"span","value":": Libraries such as "},{"type":"span","marks":["code"],"value":"SciPy"},{"type":"span","value":" and "},{"type":"span","marks":["code"],"value":"StatsModels"},{"type":"span","value":" provide built-in functions for calculating confidence intervals efficiently."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Custom Implementation"},{"type":"span","value":": For more complex models or unique requirements, Python allows for the custom implementation of confidence interval calculations."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Leveraging these tools streamlines the process of quantifying uncertainty in machine learning models."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"The Impact of Confidence Level Choices"}]},{"type":"paragraph","children":[{"type":"span","value":"The choice of confidence level (e.g., 95% or 99%) significantly influences the width of the confidence interval:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Higher Confidence Level"},{"type":"span","value":": Results in a wider confidence interval, indicating greater uncertainty."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Lower Confidence Level"},{"type":"span","value":": Leads to a narrower confidence interval, suggesting more precision but potentially overlooking the true parameter value."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Selecting the appropriate confidence level hinges on the specific context and requirements of the machine learning task at hand, balancing the trade-off between precision and reliability."}]},{"type":"paragraph","children":[{"type":"span","value":"By weaving together these methodologies and considerations, machine learning practitioners can effectively calculate confidence intervals, thereby shedding light on the reliability and generalizability of their models. This foundational understanding not only enhances model evaluation but also reinforces decision-making processes in the ever-evolving landscape of machine learning."}]},{"type":"paragraph","children":[{"item":"IbSwv5QJQCyBYp86KUZZnA","type":"inlineItem"}]},{"type":"heading","level":2,"children":[{"type":"span","value":"Methods for Creating Confidence Intervals in Machine Learning"}]},{"type":"paragraph","children":[{"type":"span","value":"In the realm of machine learning, the creation of confidence intervals is paramount for interpreting the reliability and precision of model predictions and estimates. Various methods, each with its own set of assumptions and implementations, facilitate this process. By delving into the analytical, empirical, and Bayesian methods, as well as the role of simulation studies, this section elucidates the multifaceted approaches to generating confidence intervals in machine learning applications."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Analytical Method"}]},{"type":"paragraph","children":[{"type":"span","value":"The analytical method for creating confidence intervals hinges on certain assumptions about the distribution of the estimator. Key points include:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Assumption of Normality"},{"type":"span","value":": This method typically assumes that the estimator follows a normal distribution, a presumption that holds true in many practical scenarios due to the Central Limit Theorem."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Well-understood Estimator Distribution"},{"type":"span","value":": It is most effective when the distribution of the estimator and its variance are well-characterized and can be analytically described."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Application"},{"type":"span","value":": Commonly applied in scenarios where the mathematical properties of the estimator are clearly defined, such as mean or variance estimations from large sample sizes."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"This method's strength lies in its straightforward applicability and the theoretical backing it provides, offering clear, mathematically derived confidence intervals under well-defined conditions."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Empirical Method"}]},{"type":"paragraph","children":[{"type":"span","value":"The empirical method, notably the bootstrap technique, offers a flexible approach to estimating confidence intervals without stringent distributional assumptions:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Resampling with Replacement"},{"type":"span","value":": By creating numerous resampled datasets from the original data and calculating the statistic of interest, the bootstrap method builds an empirical distribution of the estimator."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Distribution Agnostic"},{"type":"span","value":": This technique does not assume a specific underlying distribution, making it highly adaptable to various types of data and models."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Small Sample Sizes"},{"type":"span","value":": Particularly beneficial for complex estimators or when dealing with small datasets where traditional analytical methods may falter."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Reference to the bootstrap confidence interval technique showcases its practical utility in machine learning, highlighting its capacity to handle the uncertainty of predictions in a data-driven manner."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Bayesian Method"}]},{"type":"paragraph","children":[{"type":"span","value":"Incorporating prior knowledge and beliefs, the Bayesian method for confidence intervals introduces a probabilistic interpretation to the estimation process:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Prior Information"},{"type":"span","value":": By integrating prior knowledge about the parameters through a prior distribution, this method refines the estimation process based on observed data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Probabilistic Interpretation"},{"type":"span","value":": Offers a Bayesian credible interval, which provides a probabilistic range within which the true parameter value is expected to lie, given the observed data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Flexibility"},{"type":"span","value":": This approach allows for the incorporation of new evidence, updating the confidence (credible) intervals as more data become available."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"The Bayesian method exemplifies the fusion of prior knowledge with empirical data, offering a nuanced approach to quantifying uncertainty in machine learning models."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Role of Simulation Studies"}]},{"type":"paragraph","children":[{"type":"span","value":"Simulation studies play a crucial role in understanding the behavior of confidence intervals under various model assumptions and data scenarios:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Model Assumptions"},{"type":"span","value":": By simulating data under controlled conditions, researchers can assess how well confidence intervals perform under different model assumptions."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Data Scenarios"},{"type":"span","value":": Simulation enables the exploration of confidence interval behavior in diverse data conditions, including skewed distributions, outliers, or correlated variables."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Insights and Validation"},{"type":"span","value":": These studies provide valuable insights into the robustness and reliability of confidence interval methods, guiding the choice of appropriate techniques for specific machine learning problems."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Software Packages and Libraries"}]},{"type":"paragraph","children":[{"type":"span","value":"The implementation of these methods is facilitated by various software packages and libraries in Python and R, catering to the needs of the machine learning community:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Python Libraries"},{"type":"span","value":": Tools like "},{"type":"span","marks":["code"],"value":"SciPy"},{"type":"span","value":" for analytical methods, "},{"type":"span","marks":["code"],"value":"bootstrapped"},{"type":"span","value":" for the bootstrap technique, and "},{"type":"span","marks":["code"],"value":"PyMC3"},{"type":"span","value":" for Bayesian approaches enable efficient computation of confidence intervals."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"R Packages"},{"type":"span","value":": Similar capabilities are available in R, with packages such as "},{"type":"span","marks":["code"],"value":"boot"},{"type":"span","value":" for bootstrap intervals and "},{"type":"span","marks":["code"],"value":"rstan"},{"type":"span","value":" for Bayesian analysis, among others."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Examples from the Community"},{"type":"span","value":": Both Python and R are widely used in the machine learning community, with numerous examples and tutorials available to guide practitioners in applying these methods to real-world datasets."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Trade-offs"}]},{"type":"paragraph","children":[{"type":"span","value":"When choosing a method for creating confidence intervals in machine learning, several trade-offs must be considered:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Computational Complexity"},{"type":"span","value":": Empirical and Bayesian methods, while powerful, can be computationally intensive, especially with large datasets or complex models."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Accuracy"},{"type":"span","value":": The precision of the confidence intervals can vary significantly between methods, influenced by the underlying assumptions and the nature of the data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Interpretability"},{"type":"span","value":": The ease of interpreting and communicating the results of different methods can affect their suitability for certain applications or audiences."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"By carefully navigating these trade-offs, machine learning practitioners can select the most appropriate method for creating confidence intervals, balancing computational demands with the need for accuracy and interpretability. Through the judicious application of analytical, empirical, and Bayesian methods, alongside insights from simulation studies, the field continues to advance our understanding of uncertainty quantification in machine learning models."}]},{"type":"paragraph","children":[{"item":"FaceuzhAQRGLZjVVvAu5fQ","type":"inlineItem"}]},{"type":"heading","level":2,"children":[{"type":"span","value":"Applications of Confidence Intervals in Machine Learning"}]},{"type":"paragraph","children":[{"type":"span","value":"Confidence intervals provide a statistical framework that is instrumental across various facets of machine learning. Their applications range from hypothesis testing and model comparison to domain-specific implementations and enhancing the communication of machine learning results. Understanding these applications underscores the value of confidence intervals in navigating the uncertainties inherent in machine learning predictions and estimations."}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Hypothesis Testing within Machine Learning"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Assessing Model Improvements"},{"type":"span","value":": Confidence intervals are pivotal in determining whether changes in a model's performance are statistically significant or merely due to random fluctuations in the data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Feature Importance"},{"type":"span","value":": By constructing confidence intervals around feature importance scores, machine learning practitioners can discern which features contribute meaningfully to the model's predictions."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Example"},{"type":"span","value":": In a study examining the accuracy of different classifiers, confidence intervals enabled researchers to assert with 95% certainty which classifiers performed significantly better than others."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Model Comparison"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Statistical Basis for Comparison"},{"type":"span","value":": Confidence intervals facilitate a rigorous statistical comparison between models, beyond mere point estimates of performance metrics."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Informed Decision-Making"},{"type":"span","value":": By quantifying the uncertainty around model performance metrics, stakeholders can make more informed choices about which model to deploy in production environments."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Case Study"},{"type":"span","value":": Research demonstrated that when comparing deep learning models to traditional machine learning models, confidence intervals around accuracy metrics provided insights into the reliability of model superiority claims."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Domain-Specific Applications"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Personalized Medicine"},{"type":"span","value":": In the realm of personalized medicine, confidence intervals help quantify the uncertainty of predictions for individual patients, thereby guiding treatment decisions with a clearer understanding of risk."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Financial Forecasting"},{"type":"span","value":": Confidence intervals are employed to assess the reliability of financial forecasts, enabling businesses to plan with a degree of certainty about future economic conditions."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Environmental Modeling"},{"type":"span","value":": Predicting climate change impacts benefits from confidence intervals by providing a range within which predicted outcomes are likely to fall, thus aiding policy formulation."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","value":"Deep Learning"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","marks":["strong"],"value":"Uncertainty in Predictions"},{"type":"span","value":": Deep learning models, known for their complexity, often yield predictions that are hard to interpret; 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