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Morten Hjorth-Jensen
2024-09-09 13:11:22 +02:00
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@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Project 1 on Machine Learning, deadline October 7 (midnight), 2024" href="project1.html" />
<link rel="next" title="Exercises week 38" href="exercisesweek38.html" />
<link rel="prev" title="Exercises week 37" href="exercisesweek37.html" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="docsearch:language" content="None">
@@ -288,6 +288,11 @@ const thebe_selector_output = ".output, .cell_output"
Week 37: Statistical interpretations and Resampling Methods
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek38.html">
Exercises week 38
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<p aria-level="2" class="caption" role="heading">
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@@ -961,9 +966,9 @@ doconce format html week37.do.txt --no_mako -->
<!-- todo add link to videos and add link to Van Wieringens notes --><div class="section" id="plans-for-week-37-lecture-monday">
<h2>Plans for week 37, lecture Monday<a class="headerlink" href="#plans-for-week-37-lecture-monday" title="Permalink to this headline"></a></h2>
<p><strong>Material for the lecture on Monday September 9.</strong></p>
<!-- * [Video of Lecture](https://youtu.be/YOBBr_toYxc) -->
<!-- * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf) -->
<ul class="simple">
<li><p><a class="reference external" href="https://youtu.be/omLmp_kkie0">Video of Lecture</a></p></li>
<li><p><a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember9.pdf">Whiteboard notes</a></p></li>
<li><p>Statistical interpretation of Ridge and Lasso regression, see also slides from last week</p></li>
<li><p>Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff (this may partly be discussed during the exercise sessions as well.</p></li>
<li><p>Readings and Videos:</p>
@@ -1618,7 +1623,7 @@ 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
100.057 14.8058 100.061 0.148629
100.106 15.0037 100.104 0.149019
</pre></div>
</div>
</div>
@@ -1843,7 +1848,9 @@ Error: 0.10398646080125035
Bias^2: 0.1007711427354898
Var: 0.0032153180657605116
0.10398646080125035 &gt;= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
Polynomial degree: 3
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 3
Error: 0.06547790180152355
Bias^2: 0.06208238634231949
Var: 0.0033955154592040936
@@ -1875,7 +1882,9 @@ Error: 0.017355848195593347
Bias^2: 0.010331721306655127
Var: 0.007024126888938232
0.017355848195593347 &gt;= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
Polynomial degree: 9
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 9
Error: 0.02660572763718093
Bias^2: 0.010018312644137363
Var: 0.016587414993043573
@@ -1904,7 +1913,7 @@ Var: 0.20867052175034223
0.22842468702219465 &gt;= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
</pre></div>
</div>
<img alt="_images/week37_139_3.png" src="_images/week37_139_3.png" />
<img alt="_images/week37_139_5.png" src="_images/week37_139_5.png" />
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@@ -2300,12 +2309,12 @@ 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
Degree of polynomial: 13
Mean squared error on training data: 0.00781918
Mean squared error on test data: 0.56965674
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 14
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 13
Mean squared error on training data: 0.00781918
Mean squared error on test data: 0.56965674
Degree of polynomial: 14
Mean squared error on training data: 0.00465099
Mean squared error on test data: 0.28443039
Degree of polynomial: 15
@@ -2363,9 +2372,9 @@ Mean squared error on training data: 0.00063866
Mean squared error on test data: 3099.60342978
</pre></div>
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<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
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92606/626635268.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_88787/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92606/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
</pre></div>
</div>
@@ -2450,7 +2459,7 @@ Mean squared error on test data: 3099.60342978
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<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_88787/3817475779.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_92606/3817475779.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>
@@ -2644,10 +2653,10 @@ This means the variance we obtain with the standard OLS will always for <span cl
<p class="prev-next-title">Exercises week 37</p>
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