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Morten Hjorth-Jensen
2024-10-21 13:45:48 +02:00
parent 0a03ba583c
commit de6a6d8bcb
144 changed files with 7186 additions and 4274 deletions
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doc/LectureNotes/_build/html/week37.html
+52 -43
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@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek43.html">
Exercises week 43
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -1679,7 +1684,7 @@ 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
99.9716 15.1579 99.9734 0.151892
100.052 15.0095 100.051 0.150055
</pre></div>
</div>
</div>
@@ -1904,7 +1909,9 @@ 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
@@ -1914,14 +1921,14 @@ Error: 0.06844519414009445
Bias^2: 0.06453579006728324
Var: 0.003909404072811226
0.06844519414009445 &gt;= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
Polynomial degree: 5
Error: 0.05227921801205686
Bias^2: 0.0481872773043029
Var: 0.004091940707753939
0.05227921801205686 &gt;= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
Polynomial degree: 6
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 6
Error: 0.037813671417389005
Bias^2: 0.033657685071527665
Var: 0.00415598634586135
@@ -1931,7 +1938,9 @@ Error: 0.02760977349102253
Bias^2: 0.022999498260366312
Var: 0.004610275230656212
0.02760977349102253 &gt;= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525
Polynomial degree: 8
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 8
Error: 0.017355848195593347
Bias^2: 0.010331721306655127
Var: 0.007024126888938232
@@ -1951,21 +1960,21 @@ Error: 0.07160048164233104
Bias^2: 0.014436800088904942
Var: 0.05716368155342608
0.07160048164233104 &gt;= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
</pre></div>
</div>
<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
0.11547777218872497 &gt;= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
Polynomial degree: 13
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
Error: 0.22842468702219465
Bias^2: 0.01975416527185249
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" />
</div>
</div>
</div>
@@ -2302,12 +2311,12 @@ Mean squared error on test data: 129963.83146596
Degree of polynomial: 3
Mean squared error on training data: 9054.61775176
Mean squared error on test data: 10572.87627342
Degree of polynomial: 4
Mean squared error on training data: 302.15313054
Mean squared error on test data: 433.26292364
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 5
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 4
Mean squared error on training data: 302.15313054
Mean squared error on test data: 433.26292364
Degree of polynomial: 5
Mean squared error on training data: 3.64316192
Mean squared error on test data: 7.23528337
Degree of polynomial: 6
@@ -2316,12 +2325,12 @@ Mean squared error on test data: 10.50427787
Degree of polynomial: 7
Mean squared error on training data: 0.47313680
Mean squared error on test data: 1.53738247
Degree of polynomial: 8
Mean squared error on training data: 0.04926746
Mean squared error on test data: 0.14629156
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 9
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 8
Mean squared error on training data: 0.04926746
Mean squared error on test data: 0.14629156
Degree of polynomial: 9
Mean squared error on training data: 0.02546675
Mean squared error on test data: 0.11202337
Degree of polynomial: 10
@@ -2330,12 +2339,12 @@ Mean squared error on test data: 0.22467274
Degree of polynomial: 11
Mean squared error on training data: 0.01594452
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
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>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
Degree of polynomial: 14
@@ -2344,12 +2353,12 @@ Mean squared error on test data: 0.28443039
Degree of polynomial: 15
Mean squared error on training data: 0.00420072
Mean squared error on test data: 568.47051432
Degree of polynomial: 16
Mean squared error on training data: 0.00325450
Mean squared error on test data: 48.97630233
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 17
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 16
Mean squared error on training data: 0.00325450
Mean squared error on test data: 48.97630233
Degree of polynomial: 17
Mean squared error on training data: 0.00242954
Mean squared error on test data: 2.52780600
Degree of polynomial: 18
@@ -2358,12 +2367,12 @@ Mean squared error on test data: 429.25695398
Degree of polynomial: 19
Mean squared error on training data: 0.00154853
Mean squared error on test data: 239.97065359
Degree of polynomial: 20
Mean squared error on training data: 0.00140846
Mean squared error on test data: 1350.24493666
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 21
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 20
Mean squared error on training data: 0.00140846
Mean squared error on test data: 1350.24493666
Degree of polynomial: 21
Mean squared error on training data: 0.00119688
Mean squared error on test data: 1840.50530832
Degree of polynomial: 22
@@ -2372,12 +2381,12 @@ Mean squared error on test data: 1184.60929685
Degree of polynomial: 23
Mean squared error on training data: 0.00089193
Mean squared error on test data: 3892.17483760
Degree of polynomial: 24
Mean squared error on training data: 0.00083355
Mean squared error on test data: 1332.46736215
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 24
Mean squared error on training data: 0.00083355
Mean squared error on test data: 1332.46736215
Degree of polynomial: 25
Mean squared error on training data: 0.00079904
Mean squared error on test data: 7577.76690383
Degree of polynomial: 26
@@ -2386,19 +2395,19 @@ 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
Degree of polynomial: 28
Mean squared error on training data: 0.00063362
Mean squared error on test data: 674.79633065
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 28
Mean squared error on training data: 0.00063362
Mean squared error on test data: 674.79633065
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_87545/626635268.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_94293/626635268.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_87545/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94293/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
</pre></div>
</div>
@@ -2483,7 +2492,7 @@ 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_87545/3817475779.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_94293/3817475779.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>