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Morten Hjorth-Jensen
2024-10-28 06:15:26 +01:00
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@@ -348,6 +348,11 @@ const thebe_selector_output = ".output, .cell_output"
Exercises week 43
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<a class="reference internal" href="week44.html">
Week 44, Convolutional Neural Networks (CNN)
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@@ -884,10 +889,10 @@ 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: 0.147161 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.156654 sec
Jackknife Statistics :
original bias std. error
100.113 100.103 0.15078
100.193 100.183 0.150667
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@@ -1106,7 +1111,7 @@ 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
99.966 14.8724 99.9645 0.146212
100.159 15.0085 100.157 0.150625
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@@ -1318,9 +1323,7 @@ Error: 0.10398646080125035
Bias^2: 0.1007711427354898
Var: 0.0032153180657605116
0.10398646080125035 &gt;= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 3
Polynomial degree: 3
Error: 0.06547790180152355
Bias^2: 0.06208238634231949
Var: 0.0033955154592040936
@@ -1335,7 +1338,9 @@ Error: 0.05227921801205686
Bias^2: 0.0481872773043029
Var: 0.004091940707753939
0.05227921801205686 &gt;= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
Polynomial degree: 6
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<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
@@ -1350,9 +1355,7 @@ Error: 0.017355848195593347
Bias^2: 0.010331721306655127
Var: 0.007024126888938232
0.017355848195593347 &gt;= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 9
Polynomial degree: 9
Error: 0.02660572763718093
Bias^2: 0.010018312644137363
Var: 0.016587414993043573
@@ -1369,7 +1372,9 @@ Error: 0.07160048164233104
Bias^2: 0.014436800088904942
Var: 0.05716368155342608
0.07160048164233104 &gt;= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
Polynomial degree: 12
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 12
Error: 0.11547777218872497
Bias^2: 0.01628578269596628
Var: 0.09919198949275869
@@ -1630,29 +1635,31 @@ Mean squared error on test data: 1.20015436
Degree of polynomial: 11
Mean squared error on training data: 0.01640891
Mean squared error on test data: 1.35533773
Degree of polynomial: 12
Mean squared error on training data: 0.00813803
Mean squared error on test data: 0.17446471
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<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: 0.00813803
Mean squared error on test data: 0.17446471
Degree of polynomial: 13
Mean squared error on training data: 0.00759119
Mean squared error on test data: 1.08131003
Degree of polynomial: 14
Mean squared error on training data: 0.00472199
Mean squared error on test data: 0.81333808
Degree of polynomial: 15
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 15
Mean squared error on training data: 0.00410478
Mean squared error on test data: 92.09163947
Degree of polynomial: 16
Mean squared error on training data: 0.00315593
Mean squared error on test data: 234.38827994
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 17
Degree of polynomial: 17
Mean squared error on training data: 0.00242999
Mean squared error on test data: 1271.34367970
Degree of polynomial: 18
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 18
Mean squared error on training data: 0.00228740
Mean squared error on test data: 108.21093775
Degree of polynomial: 19
@@ -1661,12 +1668,12 @@ Mean squared error on test data: 1385.79778008
Degree of polynomial: 20
Mean squared error on training data: 0.00137814
Mean squared error on test data: 1944.86062977
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 21
Degree of polynomial: 21
Mean squared error on training data: 0.00118584
Mean squared error on test data: 14716.58827236
Degree of polynomial: 22
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 22
Mean squared error on training data: 0.00092678
Mean squared error on test data: 877.21517262
Degree of polynomial: 23
@@ -1675,12 +1682,12 @@ Mean squared error on test data: 5567.04664255
Degree of polynomial: 24
Mean squared error on training data: 0.00084707
Mean squared error on test data: 1325.26124692
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
Degree of polynomial: 25
Mean squared error on training data: 0.00079125
Mean squared error on test data: 129012.83870189
Degree of polynomial: 26
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 26
Mean squared error on training data: 0.00076908
Mean squared error on test data: 18388.59354079
Degree of polynomial: 27
@@ -1689,16 +1696,14 @@ Mean squared error on test data: 2351.97979891
Degree of polynomial: 28
Mean squared error on training data: 0.00062592
Mean squared error on test data: 3983.63037846
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
Degree of polynomial: 29
Mean squared error on training data: 0.00060704
Mean squared error on test data: 3262.26814548
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_20789/626635268.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_94076/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_20789/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
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@@ -1932,7 +1937,7 @@ 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
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_20789/3817475779.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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@@ -2821,7 +2826,7 @@ linear system as an equation would reduce this down to
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_20789/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2965,7 +2970,7 @@ 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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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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