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Morten Hjorth-Jensen
2024-10-21 13:45:48 +02:00
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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
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<a class="reference internal" href="exercisesweek43.html">
Exercises week 43
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@@ -879,10 +884,10 @@ 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: 0.132756 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.147161 sec
Jackknife Statistics :
original bias std. error
99.9573 99.9473 0.149003
100.113 100.103 0.15078
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@@ -1101,7 +1106,7 @@ 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
100.299 15.0473 100.299 0.149379
99.966 14.8724 99.9645 0.146212
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@@ -1313,7 +1318,9 @@ Error: 0.10398646080125035
Bias^2: 0.1007711427354898
Var: 0.0032153180657605116
0.10398646080125035 &gt;= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
Polynomial degree: 3
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<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
@@ -1338,14 +1345,14 @@ 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
0.017355848195593347 &gt;= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
Polynomial degree: 9
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<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
@@ -1355,7 +1362,9 @@ Error: 0.021592704588025025
Bias^2: 0.010516485576645508
Var: 0.011076219011379514
0.021592704588025025 &gt;= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
Polynomial degree: 11
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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
@@ -1365,16 +1374,14 @@ Error: 0.11547777218872497
Bias^2: 0.01628578269596628
Var: 0.09919198949275869
0.11547777218872497 &gt;= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
Polynomial degree: 13
Error: 0.22842468702219465
Bias^2: 0.01975416527185249
Var: 0.20867052175034223
0.22842468702219465 &gt;= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
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<img alt="_images/chapter3_66_3.png" src="_images/chapter3_66_3.png" />
<img alt="_images/chapter3_66_4.png" src="_images/chapter3_66_4.png" />
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<p>The bias-variance tradeoff summarizes the fundamental tension in
@@ -1689,9 +1696,9 @@ 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_87367/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
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@@ -1925,7 +1932,7 @@ 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_94076/3817475779.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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@@ -2814,7 +2821,7 @@ 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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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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cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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model = cd_fast.enet_coordinate_descent(
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