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Morten Hjorth-Jensen
2023-09-11 07:03:15 +02:00
parent 125231ac1a
commit 006b2407fe
8 changed files with 69 additions and 74 deletions
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doc/LectureNotes/_build/html/exercisesweek37.html
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@@ -496,8 +496,7 @@ A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span>
<p>Show also that the variance is</p>
<div class="math notranslate nohighlight">
\[
\mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[ \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1} \mathbf{X}^{T} \mathbf{X} \{ [ \m\
athbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
\mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[ \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1} \mathbf{X}^{T}\mathbf{X} \{ [ \mathbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
\]</div>
<p>and it is easy to see that if the parameter <span class="math notranslate nohighlight">\(\lambda\)</span> goes to infinity then the variance of Ridge parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> goes to zero.</p>
</div>