update

Author: mhjensen

doc/HandWrittenNotes/2025/FYSSTKweek38.pdf

@@ -452,9 +452,10 @@ <h2>Plans for week 38, lecture Monday September 15<a class="headerlink" href="#p
 <li><p>Statistical interpretation of OLS and various expectation values</p></li>
 <li><p>Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff</p></li>
 <li><p>The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at <a class="reference external" href="https://youtu.be/J_41Hld6tTU">https://youtu.be/J_41Hld6tTU</a></p></li>
+<li><p><a class="reference external" href="https://youtu.be/4Fo7ITVA7V4">Video of Lecture</a></p></li>
+<li><p><a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf">Whiteboard notes</a></p></li>
 </ol>
-<!-- * [Video of Lecture](https://youtu.be/omLmp_kkie0) -->
-<!-- * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember9.pdf) --></section>
+</section>
 <section id="readings-and-videos">
 <h2>Readings and Videos<a class="headerlink" href="#readings-and-videos" title="Link to this heading">#</a></h2>
 <ol class="arabic simple">
@@ -684,12 +685,12 @@ <h2>A new Cost Function<a class="headerlink" href="#a-new-cost-function" title="
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 <div class="math notranslate nohighlight">
 \[
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
 \]</div>
 <p>which becomes</p>
 <div class="math notranslate nohighlight">
 \[
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
 \]</div>
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters <span class="math notranslate nohighlight">\(\theta\)</span> we recognize our familiar OLS equation, namely</p>
 <div class="math notranslate nohighlight">