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2 changes: 1 addition & 1 deletion .nojekyll
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8 changes: 4 additions & 4 deletions schedule/slides/06-information-criteria.html
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Expand Up @@ -496,12 +496,12 @@ <h2>AIC and BIC</h2>
<p><span class="math inline">\(\textrm{AIC}/n = -2\textrm{loglikelihood}/n + 2\textrm{df}/n\)</span></p>
<p><span class="math inline">\(\textrm{BIC}/n = -2\textrm{loglikelihood}/n + 2\log(n)\textrm{df}/n\)</span></p>
<div class="fragment">
<p>In the case of a linear model with Gaussian errors,</p>
<p>In the case of a linear model with Gaussian errors and <span class="math inline">\(p\)</span> predictors</p>
<span class="math display">\[\begin{aligned}
\textrm{AIC} &amp;= -n + 2n\log(2\pi) - 2 + 2\log(n) - 2\log(RSS) + 2(p+2) \\
&amp;\propto -2\log(RSS) + 2(p+2)
\textrm{AIC}/n &amp;= \log(2\pi) + \log(RSS/n) + 2(p+1)/n \\
&amp;\propto \log(RSS) + 2(p+1)/n
\end{aligned}\]</span>
<p>( <span class="math inline">\(p+2\)</span> because of the intercept and the unknown variance)</p>
<p>( <span class="math inline">\(p+1\)</span> because of the unknown variance, intercept included in <span class="math inline">\(p\)</span> or not)</p>
</div>
<div class="fragment">
<div class="callout callout-important callout-titled callout-style-default">
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2 changes: 1 addition & 1 deletion search.json
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Expand Up @@ -221,7 +221,7 @@
"href": "schedule/slides/06-information-criteria.html#aic-and-bic",
"title": "UBC Stat406 2023W",
"section": "AIC and BIC",
"text": "AIC and BIC\nThese have a very similar flavor to \\(C_p\\), but their genesis is different.\nWithout going into too much detail, they look like\n\\(\\textrm{AIC}/n = -2\\textrm{loglikelihood}/n + 2\\textrm{df}/n\\)\n\\(\\textrm{BIC}/n = -2\\textrm{loglikelihood}/n + 2\\log(n)\\textrm{df}/n\\)\n\nIn the case of a linear model with Gaussian errors,\n\\[\\begin{aligned}\n\\textrm{AIC} &= -n + 2n\\log(2\\pi) - 2 + 2\\log(n) - 2\\log(RSS) + 2(p+2) \\\\\n&\\propto -2\\log(RSS) + 2(p+2)\n\\end{aligned}\\]\n( \\(p+2\\) because of the intercept and the unknown variance)\n\n\n\n\n\n\n\n\nImportant\n\n\nUnfortunately, different books/software/notes define these differently. Even different R packages. This is super annoying.\nForms above are in [ESL] eq. (7.29) and (7.35). [ISLR] gives special cases in Section 6.1.3. Remember the generic form here."
"text": "AIC and BIC\nThese have a very similar flavor to \\(C_p\\), but their genesis is different.\nWithout going into too much detail, they look like\n\\(\\textrm{AIC}/n = -2\\textrm{loglikelihood}/n + 2\\textrm{df}/n\\)\n\\(\\textrm{BIC}/n = -2\\textrm{loglikelihood}/n + 2\\log(n)\\textrm{df}/n\\)\n\nIn the case of a linear model with Gaussian errors and \\(p\\) predictors\n\\[\\begin{aligned}\n\\textrm{AIC}/n &= \\log(2\\pi) + \\log(RSS/n) + 2(p+1)/n \\\\\n&\\propto \\log(RSS) + 2(p+1)/n\n\\end{aligned}\\]\n( \\(p+1\\) because of the unknown variance, intercept included in \\(p\\) or not)\n\n\n\n\n\n\n\n\nImportant\n\n\nUnfortunately, different books/software/notes define these differently. Even different R packages. This is super annoying.\nForms above are in [ESL] eq. (7.29) and (7.35). [ISLR] gives special cases in Section 6.1.3. Remember the generic form here."
},
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"objectID": "schedule/slides/06-information-criteria.html#over-fitting-vs.-under-fitting",
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50 changes: 25 additions & 25 deletions sitemap.xml
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