updating notes

doc/LectureNotes/_build/html/week37.html

@@ -1249,12 +1249,12 @@ logarithm of the posterior probability and leaving out the
 constants terms that do not depend on <span class="math notranslate nohighlight">\(\beta\)</span>, we have</p>
 <div class="math notranslate nohighlight">
 \[
-C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
 \]</div>
 <p>and replacing <span class="math notranslate nohighlight">\(1/\tau\)</span> with <span class="math notranslate nohighlight">\(\lambda\)</span> we have</p>
 <div class="math notranslate nohighlight">
 \[
-C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
 \]</div>
 <p>which is our Lasso cost function!</p>
 </div>
@@ -1618,7 +1618,7 @@ theorem.</p>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
 original           bias      std. error
- 99.7503  14.9999        99.7496        0.151068
+ 100.057  14.8058        100.061        0.148629
 </pre></div>
 </div>
 </div>
@@ -1853,7 +1853,9 @@ Error: 0.06844519414009445
 Bias^2: 0.06453579006728324
 Var: 0.003909404072811226
 0.06844519414009445 &gt;= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
-Polynomial degree: 5
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
 Error: 0.05227921801205686
 Bias^2: 0.0481872773043029
 Var: 0.004091940707753939
@@ -1902,7 +1904,7 @@ Var: 0.20867052175034223
 0.22842468702219465 &gt;= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
 </pre></div>
 </div>
-<img alt="_images/week37_139_2.png" src="_images/week37_139_2.png" />
+<img alt="_images/week37_139_3.png" src="_images/week37_139_3.png" />
 </div>
 </div>
 </div>
@@ -2298,12 +2300,12 @@ Mean squared error on test data: 1.07641937
 Degree of polynomial:  12
 Mean squared error on training data: 0.00805074
 Mean squared error on test data: 0.04295757
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  13
+Degree of polynomial:  13
 Mean squared error on training data: 0.00781918
 Mean squared error on test data: 0.56965674
-Degree of polynomial:  14
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  14
 Mean squared error on training data: 0.00465099
 Mean squared error on test data: 0.28443039
 Degree of polynomial:  15
@@ -2351,19 +2353,19 @@ Mean squared error on test data: 1079.36895644
 Degree of polynomial:  27
 Mean squared error on training data: 0.00068091
 Mean squared error on test data: 3207.25343155
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  28
+Degree of polynomial:  28
 Mean squared error on training data: 0.00063362
 Mean squared error on test data: 674.79633065
-Degree of polynomial:  29
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  29
 Mean squared error on training data: 0.00063866
 Mean squared error on test data: 3099.60342978
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87621/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_88787/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(trainingerror), label=&#39;Training Error&#39;)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87621/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_88787/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
 </pre></div>
 </div>
@@ -2448,7 +2450,7 @@ Mean squared error on test data: 3099.60342978
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87621/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_88787/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(estimated_mse_sklearn), label=&#39;Test Error&#39;)
 </pre></div>
 </div>

doc/LectureNotes/_build/jupyter_execute/week37.py

@@ -349,13 +349,13 @@
 # constants terms that do not depend on $\beta$, we have
 
 # $$
-# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
 # $$
 
 # and replacing $1/\tau$ with $\lambda$ we have
 
 # $$
-# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
 # $$
 
 # which is our Lasso cost function!