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Morten Hjorth-Jensen
2023-11-08 15:57:33 +01:00
parent 2edd177646
commit 3b9f0dbb29
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@@ -343,6 +343,16 @@ const thebe_selector_output = ".output, .cell_output"
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
</a>
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<li class="toctree-l1">
<a class="reference internal" href="week44.html">
Week 44, Convolutional Neural Networks (CNN)
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<li class="toctree-l1">
<a class="reference internal" href="week45.html">
Week 45, Recurrent Neural Networks
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</ul>
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@@ -879,10 +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: 0.134565 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.155664 sec
Jackknife Statistics :
original bias std. error
100.2 100.19 0.146591
99.9688 99.9588 0.15043
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@@ -1101,7 +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
99.9919 15.0954 99.9924 0.150989
100.132 14.8115 100.132 0.147896
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@@ -1345,14 +1355,14 @@ Error: 0.017355848195593312
Bias^2: 0.010331721306655165
Var: 0.007024126888938144
0.017355848195593312 &gt;= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331
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: 0.026605727637184558
Bias^2: 0.010018312644139219
Var: 0.016587414993045335
0.026605727637184558 &gt;= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 10
Polynomial degree: 10
Error: 0.021592704588021178
Bias^2: 0.010516485576646504
Var: 0.01107621901137467
@@ -1670,12 +1680,12 @@ Mean squared error on test data: 128664.31650694
Degree of polynomial: 26
Mean squared error on training data: 0.00076905
Mean squared error on test data: 19003.94822514
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 27
Degree of polynomial: 27
Mean squared error on training data: 0.00068946
Mean squared error on test data: 2379.66219404
Degree of polynomial: 28
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 28
Mean squared error on training data: 0.00062595
Mean squared error on test data: 4082.19983530
Degree of polynomial: 29
@@ -1683,9 +1693,9 @@ Mean squared error on training data: 0.00060705
Mean squared error on test data: 3250.17647619
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/626635268.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_8674/626635268.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_10962/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
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@@ -1919,7 +1929,7 @@ 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_8674/3817475779.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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@@ -2808,9 +2818,9 @@ 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_8674/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
cb = fig.colorbar(im)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2954,9 +2964,9 @@ with the form utilized in linear regression, viz.</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_10962/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
cb = fig.colorbar(im)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -2996,9 +3006,9 @@ cost function is given by</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_10962/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
cb = fig.colorbar(im)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -3033,9 +3043,9 @@ cost function is given by</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_10962/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
cb = fig.colorbar(im)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
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@@ -3088,43 +3098,43 @@ 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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@@ -3271,9 +3281,9 @@ which polynomial fits the data best.</p>
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ax = fig.gca(projection=&#39;3d&#39;)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10962/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_8674/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
fig.colorbar(surf, shrink=0.5, aspect=5)
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