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Morten Hjorth-Jensen
2021-10-19 08:42:04 +02:00
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commit a0360cf460
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doc/LectureNotes/_build/html/chapteroptimization.html
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@@ -218,6 +218,11 @@
14. Building a Feed Forward Neural Network
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter11.html">
15. Solving Differential Equations with Deep Learning
</a>
</li>
</ul>
</div>
@@ -747,7 +752,7 @@ which equals</p>
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<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7f88524ba760&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7fc6b1bd1790&gt;
</pre></div>
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<img alt="_images/chapteroptimization_56_1.png" src="_images/chapteroptimization_56_1.png" />
@@ -805,7 +810,7 @@ which equals</p>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f8830b3a340&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7fc6a0739340&gt;]
</pre></div>
</div>
<img alt="_images/chapteroptimization_64_1.png" src="_images/chapteroptimization_64_1.png" />
@@ -1062,11 +1067,11 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.3043053 4.29737229]
[[3.61825186]
[3.29748212]]
[[3.61825186]
[3.29748212]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.30875823 4.41879302]
[[3.96285336]
[3.28329188]]
[[3.96285336]
[3.28329188]]
</pre></div>
</div>
<img alt="_images/chapteroptimization_118_1.png" src="_images/chapteroptimization_118_1.png" />
@@ -1095,9 +1100,9 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.3498837 ]
[2.67298546]]
[4.35386868] [2.68386076]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.75582035]
[3.15167261]]
[3.7821634] [3.18303503]
</pre></div>
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@@ -1168,10 +1173,10 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.08429424]
[2.91960881]]
[[4.00717152]
[2.97900797]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.05636001]
[2.75240368]]
[[3.99394477]
[2.80463702]]
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<img alt="_images/chapteroptimization_127_1.png" src="_images/chapteroptimization_127_1.png" />
@@ -1396,18 +1401,18 @@ function.</p>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[3.73153522]
[3.18123182]]
[[3.88168518]
[3.04348504]]
sgdreg from scikit
[3.75322913] [3.21698969]
[3.92115534] [3.13964362]
theta from own gd
[[3.73153522]
[3.18123182]]
theta from own sdg
[[3.88168518]
[3.04348504]]
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.68887763]
[3.17666625]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
[[3.92555588]
[3.0163616 ]]
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<img alt="_images/chapteroptimization_141_2.png" src="_images/chapteroptimization_141_2.png" />
@@ -1799,9 +1804,7 @@ being differentiated with respect to.</p>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Evaluating at x1 = 1, x2 = 3
------------------------------
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The derivative of f2 w.r.t x1: 12
The derivative of f2 w.r.t x1: 12
The analytical derivative of f2 w.r.t x1: 12
The derivative of f2 w.r.t x2: -4