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Morten Hjorth-Jensen
2024-11-25 08:12:27 +01:00
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commit c8f2aa3dc1
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@@ -257,6 +257,9 @@
<li class="toctree-l1"><a class="reference internal" href="week47.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek47.html">Exercise week 47</a></li>
<li class="toctree-l1"><a class="reference internal" href="week48.html">Week 48: Gradient boosting and summary of course</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek48.html">Exercises week 48</a></li>
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
<ul class="nav bd-sidenav">
@@ -726,10 +729,10 @@ number <span class="math notranslate nohighlight">\(i\)</span> is left out. Usin
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.177848 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.154011 sec
Jackknife Statistics :
original bias std. error
99.9735 99.9635 0.149504
100.105 100.095 0.14726
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@@ -948,7 +951,7 @@ theorem.</p>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
original bias std. error
99.9629 14.9658 99.9626 0.148488
100.182 15.0891 100.184 0.15218
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@@ -970,7 +973,7 @@ original bias std. error
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<img alt="_images/1f1e999736d47a2811569158c3eb924dab62b0f520b0f854e48f2e2dbb32e047.png" src="_images/1f1e999736d47a2811569158c3eb924dab62b0f520b0f854e48f2e2dbb32e047.png" />
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</section>
@@ -1155,9 +1158,7 @@ Error: 0.08426840630693411
Bias^2: 0.0796891867672603
Var: 0.004579219539673834
0.08426840630693411 &gt;= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 2
Polynomial degree: 2
Error: 0.10398646080125035
Bias^2: 0.1007711427354898
Var: 0.0032153180657605116
@@ -1189,9 +1190,7 @@ Error: 0.02760977349102253
Bias^2: 0.022999498260366312
Var: 0.004610275230656212
0.02760977349102253 &gt;= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 8
Polynomial degree: 8
Error: 0.017355848195593347
Bias^2: 0.010331721306655127
Var: 0.007024126888938232
@@ -1206,14 +1205,14 @@ Error: 0.021592704588025025
Bias^2: 0.010516485576645508
Var: 0.011076219011379514
0.021592704588025025 &gt;= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
Polynomial degree: 11
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 11
Error: 0.07160048164233104
Bias^2: 0.014436800088904942
Var: 0.05716368155342608
0.07160048164233104 &gt;= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 12
Polynomial degree: 12
Error: 0.11547777218872497
Bias^2: 0.01628578269596628
Var: 0.09919198949275869
@@ -1540,9 +1539,9 @@ Mean squared error on training data: 0.00060704
Mean squared error on test data: 3262.26814548
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plt.plot(polynomial, np.log10(trainingerror), label=&#39;Training Error&#39;)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58812/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_23110/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
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@@ -1776,7 +1775,7 @@ cross-validation (LOOCV).</p>
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_23110/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label=&#39;Test Error&#39;)
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@@ -2665,7 +2664,7 @@ linear system as an equation would reduce this down to
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cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2809,7 +2808,7 @@ with the form utilized in linear regression, viz.</p>
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cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2849,7 +2848,7 @@ cost function is given by</p>
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cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2937,43 +2936,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
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model = cd_fast.enet_coordinate_descent(
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