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Morten Hjorth-Jensen
2024-09-11 05:36:59 +02:00
parent 19a064b629
commit 3b762e5606
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@@ -824,10 +824,10 @@ 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: 0.14708 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.165272 sec
Jackknife Statistics :
original bias std. error
100.034 100.024 0.147836
99.6801 99.6702 0.149483
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@@ -1046,7 +1046,7 @@ 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
100.179 15.0422 100.179 0.151522
100.121 15.022 100.121 0.149904
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@@ -1263,14 +1263,14 @@ Error: 0.06547790180152355
Bias^2: 0.06208238634231949
Var: 0.0033955154592040936
0.06547790180152355 &gt;= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359
Polynomial degree: 4
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 4
Error: 0.06844519414009445
Bias^2: 0.06453579006728324
Var: 0.003909404072811226
0.06844519414009445 &gt;= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
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<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
@@ -1280,7 +1280,9 @@ Error: 0.037813671417389005
Bias^2: 0.033657685071527665
Var: 0.00415598634586135
0.037813671417389005 &gt;= 0.033657685071527665 + 0.00415598634586135 = 0.03781367141738902
Polynomial degree: 7
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 7
Error: 0.02760977349102253
Bias^2: 0.022999498260366312
Var: 0.004610275230656212
@@ -1290,9 +1292,7 @@ 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
@@ -1307,7 +1307,9 @@ 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
@@ -1319,7 +1321,7 @@ 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
@@ -1634,9 +1636,9 @@ 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_1390/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_6403/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
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@@ -1870,7 +1872,7 @@ 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_6403/3817475779.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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@@ -2759,7 +2761,7 @@ 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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@@ -2903,7 +2905,7 @@ 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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@@ -2943,7 +2945,7 @@ 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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@@ -3031,43 +3033,43 @@ 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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