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Morten Hjorth-Jensen
2024-09-02 16:29:05 +02:00
parent 548e735c20
commit 41f98033a3
8 changed files with 91 additions and 171 deletions
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doc/LectureNotes/_build/.doctrees/environment.pickle
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doc/LectureNotes/_build/.doctrees/exercisesweek36.doctree
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doc/LectureNotes/_build/html/_sources/exercisesweek36.ipynb
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\[
\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \left(\boldsymbol{X}^T\boldsymbol{X}+\lambda\boldsymbol{I}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y},
\]</div>
<p>with <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> being a <span class="math notranslate nohighlight">\(p\times p\)</span> identity matrix with the constraint that</p>
<div class="math notranslate nohighlight">
\[
\sum_{i=0}^{p-1} \beta_i^2 \leq t,
\]</div>
<p>with <span class="math notranslate nohighlight">\(t\)</span> a finite positive number. In the optimization, we will not require that the latter is satisfied.</p>
<p>with <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> being a <span class="math notranslate nohighlight">\(p\times p\)</span> identity matrix.</p>
<p>The ordinary least squares result is</p>
<div class="math notranslate nohighlight">
\[
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