update
This commit is contained in:
Morten Hjorth-Jensen
@@ -10,13 +10,13 @@ edge [fontname="helvetica"] ;
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2 -> 3 ;
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4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139"] ;
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3 -> 4 ;
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5 [label="area error <= 51.38\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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5 [label="mean perimeter <= 78.51\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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3 -> 5 ;
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6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ;
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5 -> 6 ;
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7 [label="gini = 0.0\nsamples = 2\nvalue = [[2, 0]\n[0, 2]]", fillcolor="#e58139"] ;
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5 -> 7 ;
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8 [label="worst texture <= 29.455\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ;
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8 [label="mean texture <= 20.84\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ;
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2 -> 8 ;
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9 [label="gini = 0.0\nsamples = 8\nvalue = [[8, 0]\n[0, 8]]", fillcolor="#e58139"] ;
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8 -> 9 ;
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@@ -30,11 +30,11 @@ edge [fontname="helvetica"] ;
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11 -> 13 ;
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14 [label="worst texture <= 20.645\ngini = 0.202\nsamples = 167\nvalue = [[19, 148]\n[148, 19]]", fillcolor="#f0b68c"] ;
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0 -> 14 [labeldistance=2.5, labelangle=-45, headlabel="False"] ;
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15 [label="worst area <= 964.4\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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15 [label="worst radius <= 17.74\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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14 -> 15 ;
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16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 0]\n[0, 11]]", fillcolor="#e58139"] ;
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15 -> 16 ;
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17 [label="symmetry error <= 0.014\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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17 [label="worst concavity <= 0.212\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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15 -> 17 ;
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18 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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17 -> 18 ;
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@@ -42,16 +42,16 @@ edge [fontname="helvetica"] ;
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17 -> 19 ;
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20 [label="mean concave points <= 0.049\ngini = 0.088\nsamples = 151\nvalue = [[7, 144]\n[144, 7]]", fillcolor="#ea985d"] ;
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14 -> 20 ;
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21 [label="compactness error <= 0.016\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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21 [label="concave points error <= 0.01\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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20 -> 21 ;
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22 [label="gini = 0.0\nsamples = 9\nvalue = [[0, 9]\n[9, 0]]", fillcolor="#e58139"] ;
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21 -> 22 ;
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23 [label="gini = 0.0\nsamples = 6\nvalue = [[6, 0]\n[0, 6]]", fillcolor="#e58139"] ;
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21 -> 23 ;
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24 [label="fractal dimension error <= 0.013\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ;
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24 [label="mean smoothness <= 0.079\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ;
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20 -> 24 ;
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25 [label="gini = 0.0\nsamples = 135\nvalue = [[0, 135]\n[135, 0]]", fillcolor="#e58139"] ;
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25 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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24 -> 25 ;
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26 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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26 [label="gini = 0.0\nsamples = 135\nvalue = [[0, 135]\n[135, 0]]", fillcolor="#e58139"] ;
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24 -> 26 ;
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}
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@@ -0,0 +1,59 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "12bcd5bb",
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"metadata": {
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"editable": true
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},
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"source": [
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"<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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"doconce format html exercisesweek39.do.txt -->\n",
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"<!-- dom:TITLE: Exercises week 39 -->"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cd59f741",
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"metadata": {
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"editable": true
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},
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"source": [
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"# Exercises week 39\n",
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"**September 23-27, 2024**\n",
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"\n",
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"Date: **Deadline is Friday September 27 at midnight**"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bdf13ce1",
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"metadata": {
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"editable": true
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},
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"source": [
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"## Overarching aims of the exercises this week\n",
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"\n",
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"The aim of the exercises this week is to aid you in getting started\n",
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||||
"with writing the report. This will be discussed during the lab\n",
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||||
"sessions as well. \n",
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"\n",
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||||
"A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
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||||
"\n",
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||||
"Similarly, an example of an earlier project can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf>\n",
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||||
"\n",
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||||
"Your task this week is to\n",
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||||
"1. Write an abstract for your project\n",
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||||
"\n",
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||||
"2. Write an introduction\n",
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||||
"\n",
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||||
"3. Include references\n",
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||||
"\n",
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||||
"A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report."
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||||
]
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||||
}
|
||||
],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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File diff suppressed because it is too large
Load Diff
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
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Week 38: Logistic Regression and Optimization
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</a>
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</li>
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||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
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<span class="caption-text">
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@@ -1026,13 +1036,13 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha:
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[1.95647867]
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[1.92622842]
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||||
Coefficient beta :
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||||
[[5.05401912]]
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||||
Mean squared error: 0.25
|
||||
[[5.21332621]]
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||||
Mean squared error: 0.22
|
||||
Variance score: 0.90
|
||||
Mean squared log error: 0.01
|
||||
Mean absolute error: 0.43
|
||||
Mean absolute error: 0.38
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter1_19_1.png" src="_images/chapter1_19_1.png" />
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@@ -1132,7 +1142,7 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
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</div>
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<div class="cell_output docutils container">
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<img alt="_images/chapter1_33_0.png" src="_images/chapter1_33_0.png" />
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.004999999999999991
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.005
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||||
</pre></div>
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||||
</div>
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||||
</div>
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
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||||
<span class="caption-text">
|
||||
@@ -1343,7 +1353,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
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</pre></div>
|
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</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
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</pre></div>
|
||||
</div>
|
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@@ -1677,7 +1687,7 @@ Lambda = 10.0
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Accuracy score on test set: 0.19166666666666668
|
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</pre></div>
|
||||
</div>
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
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return 1/(1 + np.exp(-x))
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</pre></div>
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</div>
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@@ -1686,7 +1696,7 @@ Lambda = 1e-05
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Accuracy score on test set: 0.10555555555555556
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</pre></div>
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</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
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return 1/(1 + np.exp(-x))
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</pre></div>
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</div>
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@@ -1695,7 +1705,7 @@ Lambda = 0.0001
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Accuracy score on test set: 0.08611111111111111
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</pre></div>
|
||||
</div>
|
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
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return 1/(1 + np.exp(-x))
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</pre></div>
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</div>
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@@ -1704,7 +1714,7 @@ Lambda = 0.001
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Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
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return 1/(1 + np.exp(-x))
|
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</pre></div>
|
||||
</div>
|
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@@ -1713,7 +1723,7 @@ Lambda = 0.01
|
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Accuracy score on test set: 0.08888888888888889
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</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1722,7 +1732,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1731,7 +1741,7 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
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@@ -1740,11 +1750,11 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1753,11 +1763,11 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
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/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
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/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1766,11 +1776,11 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1779,11 +1789,11 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1792,11 +1802,11 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1805,7 +1815,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1814,11 +1824,11 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1827,11 +1837,11 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1840,82 +1850,37 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95354/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">8</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">10</span> <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">11</span> <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 99,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
|
||||
<span class="ne">---> </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 64,</span> in <span class="ni">NeuralNetwork.backpropagation</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">61</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_output</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_output</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">64</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_data</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_hidden</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">65</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_hidden</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">67</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">lmbd</span> <span class="o">></span> <span class="mf">0.0</span><span class="p">:</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1961,22 +1926,6 @@ Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58656/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter10_59_1.png" src="_images/chapter10_59_1.png" />
|
||||
<img alt="_images/chapter10_59_2.png" src="_images/chapter10_59_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="scikit-learn-implementation">
|
||||
@@ -2012,326 +1961,6 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.18333333333333332
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.18611111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.13055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.24444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.23333333333333334
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.12777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.1527777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9111111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.8305555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8944444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.975
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
|
||||
Learning rate = 0.01
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9527777777777777
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9027777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8583333333333333
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9055555555555556
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8666666666666667
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.17222222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.11666666666666667
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
@@ -2375,10 +2004,6 @@ Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/chapter10_63_0.png" src="_images/chapter10_63_0.png" />
|
||||
<img alt="_images/chapter10_63_1.png" src="_images/chapter10_63_1.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
|
||||
@@ -2417,14 +2042,6 @@ and/or if you use <strong>anaconda</strong>, just write (or install from the gra
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span> <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
|
||||
<span class="n">conda</span> <span class="n">create</span> <span class="o">-</span><span class="n">n</span> <span class="n">tf</span> <span class="n">tensorflow</span>
|
||||
<span class="o">^</span>
|
||||
<span class="ne">SyntaxError</span>: invalid syntax
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>To install the current release of GPU TensorFlow</p>
|
||||
<div class="cell docutils container">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -2577,83 +2587,11 @@ Using TensorFlow results in a much better execution time. Try it!</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:28,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">21</span> <span class="nd">@unary_to_nary</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">22</span> <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">23</span><span class="w"> </span><span class="sd">"""</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">24</span><span class="sd"> Returns a function which computes the gradient of `fun` with respect to</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">25</span><span class="sd"> positional argument number `argnum`. The returned function takes the same</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">26</span><span class="sd"> arguments as `fun`, but returns the gradient instead. The function `fun`</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">27</span><span class="sd"> should be scalar-valued. The gradient has the same type as the argument."""</span>
|
||||
<span class="ne">---> </span><span class="mi">28</span> <span class="n">vjp</span><span class="p">,</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">_make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">29</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">30</span> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">"Grad only applies to real scalar-output functions. "</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">31</span> <span class="s2">"Try jacobian, elementwise_grad or holomorphic_grad."</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10,</span> in <span class="ni">make_vjp</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">def</span> <span class="nf">make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_node</span> <span class="o">=</span> <span class="n">VJPNode</span><span class="o">.</span><span class="n">new_root</span><span class="p">()</span>
|
||||
<span class="ne">---> </span><span class="mi">10</span> <span class="n">end_value</span><span class="p">,</span> <span class="n">end_node</span> <span class="o">=</span> <span class="n">trace</span><span class="p">(</span><span class="n">start_node</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">end_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">zeros</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10,</span> in <span class="ni">trace</span><span class="nt">(start_node, fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">with</span> <span class="n">trace_stack</span><span class="o">.</span><span class="n">new_trace</span><span class="p">()</span> <span class="k">as</span> <span class="n">t</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_box</span> <span class="o">=</span> <span class="n">new_box</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">start_node</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">10</span> <span class="n">end_box</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="n">start_box</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">isbox</span><span class="p">(</span><span class="n">end_box</span><span class="p">)</span> <span class="ow">and</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_trace</span> <span class="o">==</span> <span class="n">start_box</span><span class="o">.</span><span class="n">_trace</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">return</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_value</span><span class="p">,</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_node</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15,</span> in <span class="ni">unary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f</span><span class="nt">(x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">14</span> <span class="n">subargs</span> <span class="o">=</span> <span class="n">subvals</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">argnum</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
|
||||
<span class="ne">---> </span><span class="mi">15</span> <span class="k">return</span> <span class="n">fun</span><span class="p">(</span><span class="o">*</span><span class="n">subargs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[9], line 80,</span> in <span class="ni">cost_function</span><span class="nt">(P, x, t)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">78</span> <span class="n">g_t</span> <span class="o">=</span> <span class="n">g_trial</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">79</span> <span class="n">g_t_jacobian</span> <span class="o">=</span> <span class="n">g_t_jacobian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">80</span> <span class="n">g_t_hessian</span> <span class="o">=</span> <span class="n">g_t_hessian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">82</span> <span class="n">g_t_dt</span> <span class="o">=</span> <span class="n">g_t_jacobian</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="n">g_t_d2x</span> <span class="o">=</span> <span class="n">g_t_hessian</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.<locals>.nary_operator.<locals>.nary_f</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:81,</span> in <span class="ni">hessian</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">78</span> <span class="nd">@unary_to_nary</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">79</span> <span class="k">def</span> <span class="nf">hessian</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">80</span> <span class="s2">"Returns a function that computes the exact Hessian."</span>
|
||||
<span class="ne">---> </span><span class="mi">81</span> <span class="k">return</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">fun</span><span class="p">))(</span><span class="n">x</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.<locals>.nary_operator.<locals>.nary_f</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:64,</span> in <span class="ni">jacobian</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="n">jacobian_shape</span> <span class="o">=</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">63</span> <span class="n">grads</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">vjp</span><span class="p">,</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">standard_basis</span><span class="p">())</span>
|
||||
<span class="ne">---> </span><span class="mi">64</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">grads</span><span class="p">),</span> <span class="n">jacobian_shape</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni">stack</span><span class="nt">(arrays, axis)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="c1"># this code is basically copied from numpy/core/shape_base.py's stack</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">85</span> <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">86</span> <span class="c1"># primitives defined in this file</span>
|
||||
<span class="ne">---> </span><span class="mi">88</span> <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">89</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">90</span> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'need at least one array to stack'</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni"><listcomp></span><span class="nt">(.0)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="c1"># this code is basically copied from numpy/core/shape_base.py's stack</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">85</span> <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">86</span> <span class="c1"># primitives defined in this file</span>
|
||||
<span class="ne">---> </span><span class="mi">88</span> <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">89</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">90</span> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'need at least one array to stack'</span><span class="p">)</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:32,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">29</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">30</span> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">"Grad only applies to real scalar-output functions. "</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">31</span> <span class="s2">"Try jacobian, elementwise_grad or holomorphic_grad."</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">32</span> <span class="k">return</span> <span class="n">vjp</span><span class="p">(</span><span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">ones</span><span class="p">())</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14,</span> in <span class="ni">make_vjp.<locals>.vjp</span><span class="nt">(g)</span>
|
||||
<span class="ne">---> </span><span class="mi">14</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">backward_pass</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">end_node</span><span class="p">)</span>
|
||||
@@ -2678,12 +2616,30 @@ Using TensorFlow results in a much better execution time. Try it!</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">659</span> <span class="n">target_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">660</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">unbroadcast</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">),</span> <span class="n">target_meta</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:651,</span> in <span class="ni">unbroadcast</span><span class="nt">(x, target_meta, broadcast_idx)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">649</span> <span class="k">while</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">></span> <span class="n">target_ndim</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">650</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">broadcast_idx</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">651</span> <span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">size</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">target_shape</span><span class="p">):</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:653,</span> in <span class="ni">unbroadcast</span><span class="nt">(x, target_meta, broadcast_idx)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">651</span> <span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">size</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">target_shape</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">652</span> <span class="k">if</span> <span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">653</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">653</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">654</span> <span class="k">if</span> <span class="n">anp</span><span class="o">.</span><span class="n">iscomplexobj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">target_iscomplex</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">655</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48,</span> in <span class="ni">primitive.<locals>.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">46</span> <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">47</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="ne">---> </span><span class="mi">48</span> <span class="k">return</span> <span class="n">f_raw</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File <__array_function__ internals>:180,</span> in <span class="ni">sum</span><span class="nt">(*args, **kwargs)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:2296,</span> in <span class="ni">sum</span><span class="nt">(a, axis, dtype, out, keepdims, initial, where)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2293</span> <span class="k">return</span> <span class="n">out</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2294</span> <span class="k">return</span> <span class="n">res</span>
|
||||
<span class="ne">-> </span><span class="mi">2296</span> <span class="k">return</span> <span class="n">_wrapreduction</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="s1">'sum'</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="n">keepdims</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2297</span> <span class="n">initial</span><span class="o">=</span><span class="n">initial</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:86,</span> in <span class="ni">_wrapreduction</span><span class="nt">(obj, ufunc, method, axis, dtype, out, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="k">return</span> <span class="n">reduction</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">,</span> <span class="o">**</span><span class="n">passkwargs</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">86</span> <span class="k">return</span> <span class="n">ufunc</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="o">**</span><span class="n">passkwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1275,10 +1285,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.07978850553011713
|
||||
3.8232102961414203
|
||||
[[ 1.25705685 3.70704566]
|
||||
[ 3.70704566 12.1664372 ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.024792624800382218
|
||||
3.9225384545636204
|
||||
[[0.94623184 2.84401886]
|
||||
[2.84401886 9.4477214 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1315,10 +1325,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08931169286872433
|
||||
2.047447724189861
|
||||
[[1. 0.66729685]
|
||||
[0.66729685 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08536248571780691
|
||||
1.8207274870895702
|
||||
[[1. 0.74900488]
|
||||
[0.74900488 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1348,30 +1358,32 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 2.37582891 5.4242743 ]
|
||||
[-0.81925302 -3.60052901]
|
||||
[ 0.37467515 3.16158074]
|
||||
[-0.40478305 -2.22601408]
|
||||
[-0.0776532 -1.70594608]
|
||||
[-0.99434472 -2.2026985 ]
|
||||
[ 0.71376303 2.77725472]
|
||||
[ 0.94637206 2.69303453]
|
||||
[-0.19791352 0.93366198]
|
||||
[-1.91669165 -5.2546186 ]]
|
||||
0 1
|
||||
0 2.375829 5.424274
|
||||
1 -0.819253 -3.600529
|
||||
2 0.374675 3.161581
|
||||
3 -0.404783 -2.226014
|
||||
4 -0.077653 -1.705946
|
||||
5 -0.994345 -2.202698
|
||||
6 0.713763 2.777255
|
||||
7 0.946372 2.693035
|
||||
8 -0.197914 0.933662
|
||||
9 -1.916692 -5.254619
|
||||
0 1
|
||||
0 1.000000 0.932382
|
||||
1 0.932382 1.000000
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.10115017 1.66431407]
|
||||
[ 0.12043521 1.32305911]
|
||||
[-1.30023144 -3.36154104]
|
||||
[-0.25200841 -1.11277166]
|
||||
[-1.55102329 -4.20158083]
|
||||
[ 0.72770687 0.97206657]
|
||||
[ 0.76533281 2.10747579]
|
||||
[-0.20666447 0.79623487]
|
||||
[-0.63919355 -2.48490503]
|
||||
[ 1.23449607 4.29764815]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
|
||||
0 1.101150 1.664314
|
||||
1 0.120435 1.323059
|
||||
2 -1.300231 -3.361541
|
||||
3 -0.252008 -1.112772
|
||||
4 -1.551023 -4.201581
|
||||
5 0.727707 0.972067
|
||||
6 0.765333 2.107476
|
||||
7 -0.206664 0.796235
|
||||
8 -0.639194 -2.484905
|
||||
9 1.234496 4.297648
|
||||
0 1
|
||||
0 1.0000 0.9434
|
||||
1 0.9434 1.0000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1428,37 +1440,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.080947 0.086913 0.082764 0.085436 0.088029 0.075956 0.077683
|
||||
2 0.0 0.086913 0.094044 0.088199 0.091365 0.094439 0.080171 0.082174
|
||||
3 0.0 0.082764 0.088199 0.090624 0.093094 0.095465 0.086730 0.088375
|
||||
4 0.0 0.085436 0.091365 0.093094 0.095805 0.098414 0.088651 0.090440
|
||||
5 0.0 0.088029 0.094439 0.095465 0.098414 0.101263 0.090468 0.092401
|
||||
6 0.0 0.075956 0.080171 0.086730 0.088651 0.090468 0.085390 0.086712
|
||||
7 0.0 0.077683 0.082174 0.088375 0.090440 0.092401 0.086712 0.088127
|
||||
8 0.0 0.079444 0.084218 0.090038 0.092252 0.094362 0.088038 0.089548
|
||||
9 0.0 0.081252 0.086318 0.091731 0.094099 0.096365 0.089376 0.090985
|
||||
10 0.0 0.068684 0.071868 0.080702 0.082126 0.083446 0.081103 0.082115
|
||||
11 0.0 0.069978 0.073339 0.081978 0.083499 0.084915 0.082170 0.083248
|
||||
12 0.0 0.071314 0.074859 0.083288 0.084910 0.086428 0.083260 0.084406
|
||||
13 0.0 0.072697 0.076435 0.084637 0.086364 0.087988 0.084376 0.085592
|
||||
14 0.0 0.074130 0.078071 0.086026 0.087864 0.089600 0.085518 0.086809
|
||||
1 0.0 0.083179 0.086483 0.081217 0.083548 0.086239 0.072037 0.073514
|
||||
2 0.0 0.086483 0.091362 0.082533 0.085853 0.089626 0.071638 0.073800
|
||||
3 0.0 0.081217 0.082533 0.084963 0.086068 0.087429 0.079030 0.079670
|
||||
4 0.0 0.083548 0.085853 0.086068 0.087871 0.089996 0.078945 0.080094
|
||||
5 0.0 0.086239 0.089626 0.087429 0.089996 0.092956 0.079002 0.080706
|
||||
6 0.0 0.072037 0.071638 0.079030 0.078945 0.079002 0.076071 0.075876
|
||||
7 0.0 0.073514 0.073800 0.079670 0.080094 0.080706 0.075876 0.076066
|
||||
8 0.0 0.075289 0.076321 0.080549 0.081527 0.082742 0.075842 0.076448
|
||||
9 0.0 0.077391 0.079240 0.081686 0.083268 0.085145 0.075978 0.077035
|
||||
10 0.0 0.063786 0.062216 0.072380 0.071437 0.070552 0.071436 0.070622
|
||||
11 0.0 0.064606 0.063536 0.072591 0.072031 0.071560 0.071049 0.070531
|
||||
12 0.0 0.065654 0.065121 0.072997 0.072849 0.072826 0.070805 0.070605
|
||||
13 0.0 0.066948 0.067000 0.073612 0.073911 0.074374 0.070712 0.070855
|
||||
14 0.0 0.068512 0.069203 0.074454 0.075239 0.076232 0.070780 0.071294
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.079444 0.081252 0.068684 0.069978 0.071314 0.072697 0.074130
|
||||
2 0.084218 0.086318 0.071868 0.073339 0.074859 0.076435 0.078071
|
||||
3 0.090038 0.091731 0.080702 0.081978 0.083288 0.084637 0.086026
|
||||
4 0.092252 0.094099 0.082126 0.083499 0.084910 0.086364 0.087864
|
||||
5 0.094362 0.096365 0.083446 0.084915 0.086428 0.087988 0.089600
|
||||
6 0.088038 0.089376 0.081103 0.082170 0.083260 0.084376 0.085518
|
||||
7 0.089548 0.090985 0.082115 0.083248 0.084406 0.085592 0.086809
|
||||
8 0.091068 0.092607 0.083119 0.084319 0.085548 0.086808 0.088102
|
||||
9 0.092607 0.094254 0.084122 0.085392 0.086694 0.088030 0.089404
|
||||
10 0.083119 0.084122 0.078238 0.079089 0.079953 0.080832 0.081728
|
||||
11 0.084319 0.085392 0.079089 0.079989 0.080903 0.081835 0.082785
|
||||
12 0.085548 0.086694 0.079953 0.080903 0.081871 0.082857 0.083864
|
||||
13 0.086808 0.088030 0.080832 0.081835 0.082857 0.083900 0.084967
|
||||
14 0.088102 0.089404 0.081728 0.082785 0.083864 0.084967 0.086096
|
||||
1 0.075289 0.077391 0.063786 0.064606 0.065654 0.066948 0.068512
|
||||
2 0.076321 0.079240 0.062216 0.063536 0.065121 0.067000 0.069203
|
||||
3 0.080549 0.081686 0.072380 0.072591 0.072997 0.073612 0.074454
|
||||
4 0.081527 0.083268 0.071437 0.072031 0.072849 0.073911 0.075239
|
||||
5 0.082742 0.085145 0.070552 0.071560 0.072826 0.074374 0.076232
|
||||
6 0.075842 0.075978 0.071436 0.071049 0.070805 0.070712 0.070780
|
||||
7 0.076448 0.077035 0.070622 0.070531 0.070605 0.070855 0.071294
|
||||
8 0.077280 0.078359 0.069907 0.070135 0.070552 0.071173 0.072015
|
||||
9 0.078359 0.079976 0.069293 0.069866 0.070655 0.071680 0.072961
|
||||
10 0.069907 0.069293 0.068353 0.067515 0.066778 0.066145 0.065619
|
||||
11 0.070135 0.069866 0.067515 0.066912 0.066425 0.066059 0.065821
|
||||
12 0.070552 0.070655 0.066778 0.066425 0.066205 0.066127 0.066199
|
||||
13 0.071173 0.071680 0.066145 0.066059 0.066127 0.066358 0.066766
|
||||
14 0.072015 0.072961 0.065619 0.065821 0.066199 0.066766 0.067539
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -829,10 +839,10 @@ number <span class="math notranslate nohighlight">\(i\)</span> is left out. Usin
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.139224 sec
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.147545 sec
|
||||
Jackknife Statistics :
|
||||
original bias std. error
|
||||
99.9792 99.9692 0.149921
|
||||
99.977 99.967 0.152494
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1051,7 +1061,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
99.8978 15.0232 99.8962 0.149063
|
||||
100.041 14.8133 100.041 0.149266
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1263,26 +1273,26 @@ Error: 0.10398646080125035
|
||||
Bias^2: 0.1007711427354898
|
||||
Var: 0.0032153180657605116
|
||||
0.10398646080125035 >= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
0.06547790180152355 >= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359
|
||||
Polynomial degree: 4
|
||||
</pre></div>
|
||||
</div>
|
||||
<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 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
|
||||
Polynomial degree: 5
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
|
||||
Error: 0.05227921801205686
|
||||
Bias^2: 0.0481872773043029
|
||||
Var: 0.004091940707753939
|
||||
0.05227921801205686 >= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 6
|
||||
Polynomial degree: 6
|
||||
Error: 0.037813671417389005
|
||||
Bias^2: 0.033657685071527665
|
||||
Var: 0.00415598634586135
|
||||
@@ -1297,19 +1307,21 @@ Error: 0.017355848195593347
|
||||
Bias^2: 0.010331721306655127
|
||||
Var: 0.007024126888938232
|
||||
0.017355848195593347 >= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
|
||||
Polynomial degree: 9
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
0.02660572763718093 >= 0.010018312644137363 + 0.016587414993043573 = 0.026605727637180936
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 10
|
||||
Polynomial degree: 10
|
||||
Error: 0.021592704588025025
|
||||
Bias^2: 0.010516485576645508
|
||||
Var: 0.011076219011379514
|
||||
0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
|
||||
Polynomial degree: 11
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
@@ -1326,7 +1338,7 @@ Var: 0.20867052175034223
|
||||
0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter3_66_4.png" src="_images/chapter3_66_4.png" />
|
||||
<img alt="_images/chapter3_66_5.png" src="_images/chapter3_66_5.png" />
|
||||
</div>
|
||||
</div>
|
||||
<p>The bias-variance tradeoff summarizes the fundamental tension in
|
||||
@@ -1641,9 +1653,9 @@ Mean squared error on training data: 0.00060704
|
||||
Mean squared error on test data: 3262.26814548
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/626635268.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_95419/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95419/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1877,7 +1889,7 @@ cross-validation (LOOCV).</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3817475779.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_95419/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2766,7 +2778,7 @@ linear system as an equation would reduce this down to
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95419/4162706317.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)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2910,7 +2922,7 @@ with the form utilized in linear regression, viz.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95419/3777801602.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)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2950,7 +2962,7 @@ cost function is given by</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95419/438060758.py:10: 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)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2985,7 +2997,7 @@ cost function is given by</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95419/3544313922.py:9: 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)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3038,43 +3050,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
|
||||
</div>
|
||||
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|
||||
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||||
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||||
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|
||||
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|
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||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|███████████████████████████████████████████████████████████████████████████████████████████████████████▏ | 6/10 [00:04<00:02, 1.55it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|███████████████████████████████████████████████████████████████████▏ | 6/10 [00:04<00:02, 1.47it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▍ | 7/10 [00:04<00:01, 1.50it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████████████▍ | 7/10 [00:04<00:01, 1.53it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▌ | 8/10 [00:05<00:01, 1.52it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|█████████████████████████████████████████████████████████████████████████████████████████▌ | 8/10 [00:05<00:01, 1.54it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▊ | 9/10 [00:06<00:00, 1.50it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|████████████████████████████████████████████████████████████████████████████████████████████████████▊ | 9/10 [00:06<00:00, 1.49it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.52it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.45it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.47it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.43it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -757,9 +767,9 @@ predicting the target features of query instances is as follows:</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2nd degree coefficients:
|
||||
zero power: -1.4725246793626128
|
||||
first power: -0.08935132374099551
|
||||
second power: 0.00034688149480437765
|
||||
zero power: -1.5105332296929628
|
||||
first power: 0.08398399377155011
|
||||
second power: -0.0003701342170783489
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter6_1_1.png" src="_images/chapter6_1_1.png" />
|
||||
@@ -1626,9 +1636,7 @@ Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test set accuracy with SVM: 0.63
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test set accuracy with Decision Trees: 0.90
|
||||
Test set accuracy with Decision Trees: 0.90
|
||||
Test set accuracy Logistic Regression with scaled data: 0.96
|
||||
Test set accuracy SVM with scaled data: 0.96
|
||||
Test set accuracy with Decision Trees and scaled data: 0.89
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -711,10 +721,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.14934258650797513
|
||||
4.548263635652985
|
||||
[[ 1.0875061 3.3260513 ]
|
||||
[ 3.3260513 11.10994958]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.13035147135400782
|
||||
4.25879315330607
|
||||
[[0.86867512 2.59009792]
|
||||
[2.59009792 8.82533209]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -754,10 +764,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.09291556244521161
|
||||
2.096511363983559
|
||||
[[1. 0.7198234]
|
||||
[0.7198234 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08690184845323
|
||||
1.521422502348998
|
||||
[[1. 0.69768266]
|
||||
[0.69768266 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -786,30 +796,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.20480187 0.26586817]
|
||||
[ 0.72601722 1.13675593]
|
||||
[ 0.02649469 -0.9834505 ]
|
||||
[ 0.97548406 1.6266783 ]
|
||||
[-1.59078383 -4.25673276]
|
||||
[-0.40596423 -0.31486917]
|
||||
[-0.34654596 -1.94627617]
|
||||
[-1.33062878 -3.73785069]
|
||||
[ 2.22810365 9.25389111]
|
||||
[-0.48697869 -1.04401421]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.14550854 1.96870431]
|
||||
[ 0.79787194 3.11438414]
|
||||
[-0.18497496 -1.31315504]
|
||||
[-1.52706754 -4.97482498]
|
||||
[-1.30190897 -3.11113486]
|
||||
[-0.08421808 -1.70928399]
|
||||
[ 0.11992194 -0.07776381]
|
||||
[-0.90717653 -2.20404927]
|
||||
[ 1.05201041 5.38762019]
|
||||
[ 0.89003324 2.9195033 ]]
|
||||
0 1
|
||||
0 0.204802 0.265868
|
||||
1 0.726017 1.136756
|
||||
2 0.026495 -0.983450
|
||||
3 0.975484 1.626678
|
||||
4 -1.590784 -4.256733
|
||||
5 -0.405964 -0.314869
|
||||
6 -0.346546 -1.946276
|
||||
7 -1.330629 -3.737851
|
||||
8 2.228104 9.253891
|
||||
9 -0.486979 -1.044014
|
||||
0 1.145509 1.968704
|
||||
1 0.797872 3.114384
|
||||
2 -0.184975 -1.313155
|
||||
3 -1.527068 -4.974825
|
||||
4 -1.301909 -3.111135
|
||||
5 -0.084218 -1.709284
|
||||
6 0.119922 -0.077764
|
||||
7 -0.907177 -2.204049
|
||||
8 1.052010 5.387620
|
||||
9 0.890033 2.919503
|
||||
0 1
|
||||
0 1.000000 0.950423
|
||||
1 0.950423 1.000000
|
||||
0 1.000000 0.937057
|
||||
1 0.937057 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -866,37 +876,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.072147 0.072728 0.071758 0.072209 0.072843 0.064428 0.064668
|
||||
2 0.0 0.072728 0.075385 0.069979 0.071530 0.073408 0.061386 0.062260
|
||||
3 0.0 0.071758 0.069979 0.076968 0.076244 0.075522 0.072286 0.071935
|
||||
4 0.0 0.072209 0.071530 0.076244 0.076161 0.076150 0.070898 0.070950
|
||||
5 0.0 0.072843 0.073408 0.075522 0.076150 0.076934 0.069399 0.069885
|
||||
6 0.0 0.064428 0.061386 0.072286 0.070898 0.069399 0.069873 0.069179
|
||||
7 0.0 0.064668 0.062260 0.071935 0.070950 0.069885 0.069179 0.068758
|
||||
8 0.0 0.065062 0.063354 0.071655 0.071103 0.070514 0.068494 0.068360
|
||||
9 0.0 0.065616 0.064690 0.071433 0.071356 0.071291 0.067793 0.067967
|
||||
10 0.0 0.057287 0.053787 0.066153 0.064505 0.062691 0.065212 0.064382
|
||||
11 0.0 0.057387 0.054286 0.065949 0.064573 0.063048 0.064834 0.064202
|
||||
12 0.0 0.057607 0.054932 0.065830 0.064739 0.063518 0.064507 0.064077
|
||||
13 0.0 0.057951 0.055737 0.065788 0.065001 0.064107 0.064218 0.064000
|
||||
14 0.0 0.058422 0.056717 0.065818 0.065358 0.064820 0.063954 0.063959
|
||||
1 0.0 0.080345 0.078573 0.079174 0.077839 0.076679 0.070275 0.069320
|
||||
2 0.0 0.078573 0.078146 0.079202 0.078688 0.078268 0.071580 0.071186
|
||||
3 0.0 0.079174 0.079202 0.083342 0.083016 0.082784 0.076947 0.076648
|
||||
4 0.0 0.077839 0.078688 0.083016 0.083260 0.083547 0.077485 0.077601
|
||||
5 0.0 0.076679 0.078268 0.082784 0.083547 0.084312 0.078044 0.078541
|
||||
6 0.0 0.070275 0.071580 0.076947 0.077485 0.078044 0.072947 0.073258
|
||||
7 0.0 0.069320 0.071186 0.076648 0.077601 0.078541 0.073258 0.073882
|
||||
8 0.0 0.068539 0.070918 0.076479 0.077813 0.079107 0.073647 0.074561
|
||||
9 0.0 0.067922 0.070772 0.076434 0.078123 0.079747 0.074115 0.075302
|
||||
10 0.0 0.061319 0.063395 0.068977 0.070098 0.071191 0.066686 0.067431
|
||||
11 0.0 0.060726 0.063206 0.068843 0.070274 0.071656 0.066988 0.067974
|
||||
12 0.0 0.060275 0.063130 0.068827 0.070547 0.072200 0.067374 0.068587
|
||||
13 0.0 0.059956 0.063161 0.068924 0.070916 0.072824 0.067843 0.069270
|
||||
14 0.0 0.059761 0.063294 0.069129 0.071379 0.073528 0.068394 0.070024
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.065062 0.065616 0.057287 0.057387 0.057607 0.057951 0.058422
|
||||
2 0.063354 0.064690 0.053787 0.054286 0.054932 0.055737 0.056717
|
||||
3 0.071655 0.071433 0.066153 0.065949 0.065830 0.065788 0.065818
|
||||
4 0.071103 0.071356 0.064505 0.064573 0.064739 0.065001 0.065358
|
||||
5 0.070514 0.071291 0.062691 0.063048 0.063518 0.064107 0.064820
|
||||
6 0.068494 0.067793 0.065212 0.064834 0.064507 0.064218 0.063954
|
||||
7 0.068360 0.067967 0.064382 0.064202 0.064077 0.064000 0.063959
|
||||
8 0.068268 0.068206 0.063526 0.063549 0.063637 0.063781 0.063977
|
||||
9 0.068206 0.068504 0.062616 0.062853 0.063163 0.063545 0.063995
|
||||
10 0.063526 0.062616 0.061724 0.061284 0.060870 0.060471 0.060071
|
||||
11 0.063549 0.062853 0.061284 0.060994 0.060734 0.060490 0.060251
|
||||
12 0.063637 0.063163 0.060870 0.060734 0.060629 0.060547 0.060475
|
||||
13 0.063781 0.063545 0.060471 0.060490 0.060547 0.060631 0.060735
|
||||
14 0.063977 0.063995 0.060071 0.060251 0.060475 0.060735 0.061025
|
||||
1 0.068539 0.067922 0.061319 0.060726 0.060275 0.059956 0.059761
|
||||
2 0.070918 0.070772 0.063395 0.063206 0.063130 0.063161 0.063294
|
||||
3 0.076479 0.076434 0.068977 0.068843 0.068827 0.068924 0.069129
|
||||
4 0.077813 0.078123 0.070098 0.070274 0.070547 0.070916 0.071379
|
||||
5 0.079107 0.079747 0.071191 0.071656 0.072200 0.072824 0.073528
|
||||
6 0.073647 0.074115 0.066686 0.066988 0.067374 0.067843 0.068394
|
||||
7 0.074561 0.075302 0.067431 0.067974 0.068587 0.069270 0.070024
|
||||
8 0.075513 0.076508 0.068215 0.068985 0.069811 0.070696 0.071643
|
||||
9 0.076508 0.077745 0.069045 0.070027 0.071055 0.072132 0.073262
|
||||
10 0.068215 0.069045 0.061898 0.062520 0.063197 0.063933 0.064728
|
||||
11 0.068985 0.070027 0.062520 0.063332 0.064189 0.065096 0.066054
|
||||
12 0.069811 0.071055 0.063197 0.064189 0.065217 0.066286 0.067400
|
||||
13 0.070696 0.072132 0.063933 0.065096 0.066286 0.067511 0.068775
|
||||
14 0.071643 0.073262 0.064728 0.066054 0.067400 0.068775 0.070183
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1085,10 +1095,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
|
||||
0 3.935972 1.991047
|
||||
1 1.991047 2.000783
|
||||
[[3.93597168 1.99104747]
|
||||
[1.99104747 2.00078324]]
|
||||
0 4.032196 2.034476
|
||||
1 2.034476 1.997746
|
||||
[[4.0321956 2.03447649]
|
||||
[2.03447649 1.99774602]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1115,8 +1125,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
|
||||
[[3.93597168 1.99104747]
|
||||
[1.99104747 2.00078324]]
|
||||
[[4.0321956 2.03447649]
|
||||
[2.03447649 1.99774602]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
|
||||
@@ -1176,16 +1186,16 @@ questions.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
|
||||
5.182086698929565
|
||||
0.7546682196464342
|
||||
5.2895786617507
|
||||
0.7403629637766833
|
||||
First eigenvector
|
||||
[0.84767088 0.53052247]
|
||||
[0.85064942 0.52573336]
|
||||
Second eigenvector
|
||||
[-0.53052247 0.84767088]
|
||||
[-0.52573336 0.85064942]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
|
||||
[0.84767088 0.53052247]
|
||||
[-0.85064942 -0.52573336]
|
||||
</pre></div>
|
||||
</div>
|
||||
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|
||||
|
||||
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|
||||
Week 38: Logistic Regression and Optimization
|
||||
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|
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|
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Exercises week 39
|
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|
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|
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Week 39: Optimization and Gradient Methods
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Week 38: Logistic Regression and Optimization
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Exercises week 39
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Week 38: Logistic Regression and Optimization
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Week 39: Optimization and Gradient Methods
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Week 38: Logistic Regression and Optimization
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Week 38: Logistic Regression and Optimization
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Exercises week 37
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Week 38: Logistic Regression and Optimization
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Exercises week 39
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Week 39: Optimization and Gradient Methods
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<h1>Exercises week 39</h1>
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<h1>Exercises week 39<a class="headerlink" href="#exercises-week-39" title="Permalink to this headline">¶</a></h1>
|
||||
<p><strong>September 23-27, 2024</strong></p>
|
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<p>Date: <strong>Deadline is Friday September 27 at midnight</strong></p>
|
||||
<div class="section" id="overarching-aims-of-the-exercises-this-week">
|
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<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The aim of the exercises this week is to aid you in getting started
|
||||
with writing the report. This will be discussed during the lab
|
||||
sessions as well.</p>
|
||||
<p>A general guideline can be found at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md</a>.</p>
|
||||
<p>Similarly, an example of an earlier project can be found at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf</a></p>
|
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<p>Your task this week is to</p>
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||||
<ol class="simple">
|
||||
<li><p>Write an abstract for your project</p></li>
|
||||
<li><p>Write an introduction</p></li>
|
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<li><p>Include references</p></li>
|
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|
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<p>A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report.</p>
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@@ -294,6 +294,16 @@ const thebe_selector_output = ".output, .cell_output"
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Week 38: Logistic Regression and Optimization
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Exercises week 39
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Week 39: Optimization and Gradient Methods
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@@ -295,6 +295,16 @@ const thebe_selector_output = ".output, .cell_output"
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Week 38: Logistic Regression and Optimization
|
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Week 39: Optimization and Gradient Methods
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@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
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Week 38: Logistic Regression and Optimization
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Week 39: Optimization and Gradient Methods
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</ul>
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<p aria-level="2" class="caption" role="heading">
|
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<span class="caption-text">
|
||||
@@ -613,8 +623,8 @@ matrices and vectors.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.29015871 0.69417174 -1.07998756 0.34332677 0.19547923 -1.09755017
|
||||
0.86197958 -0.15546887 0.14369927 1.96251859]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 0.69465386 1.75956617 -0.23303727 -0.53125507 1.34598722 -1.09928714
|
||||
1.37013105 0.79898903 -0.23663482 0.99427512]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -835,26 +845,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.08233627 0.43727575 0.01759442 0.01179415 0.34483937 0.32733949
|
||||
0.71332117 0.20347912 0.57521514 0.56042437]
|
||||
[0.64909048 0.55179339 0.13847167 0.04224929 0.89540936 0.5142856
|
||||
0.85871255 0.75080943 0.34026086 0.50850373]
|
||||
[0.03239393 0.87884833 0.41310208 0.82418008 0.01014331 0.24284399
|
||||
0.93668828 0.79247398 0.48062913 0.77803692]
|
||||
[0.73068535 0.47910545 0.95715036 0.11844773 0.76686148 0.31453949
|
||||
0.6029291 0.5443909 0.29398019 0.96585824]
|
||||
[0.0179826 0.51643579 0.53723188 0.03844073 0.25989189 0.20834188
|
||||
0.98619989 0.40833375 0.52876551 0.76612827]
|
||||
[0.44830934 0.94099173 0.07123177 0.96305058 0.11596834 0.69756791
|
||||
0.60664448 0.89457785 0.86016288 0.33615742]
|
||||
[0.35243372 0.77465911 0.37532078 0.38399622 0.20728198 0.1108407
|
||||
0.83020679 0.48170743 0.99003341 0.99956033]
|
||||
[0.82832579 0.42553096 0.02355756 0.28542801 0.96894842 0.70711022
|
||||
0.8825782 0.04072235 0.24369936 0.79622905]
|
||||
[0.60762863 0.21699817 0.20218457 0.63071772 0.02358547 0.62886648
|
||||
0.44286735 0.78745927 0.30982436 0.76277254]
|
||||
[0.52173381 0.9495484 0.47433659 0.73203674 0.95226607 0.40072098
|
||||
0.35098705 0.46544987 0.66456459 0.25512598]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.81947005 0.93619369 0.37449168 0.91933003 0.76855921 0.41820116
|
||||
0.96853248 0.60375434 0.96015381 0.30269539]
|
||||
[0.46086448 0.16777789 0.9930742 0.10837392 0.69089532 0.94221383
|
||||
0.53629564 0.50327198 0.33734605 0.04757138]
|
||||
[0.51069279 0.12363332 0.79171202 0.16791183 0.62617788 0.9288904
|
||||
0.85112594 0.86519139 0.61192712 0.90842732]
|
||||
[0.82551764 0.67524588 0.02175561 0.1118933 0.42575338 0.45731379
|
||||
0.61069681 0.40184681 0.18702469 0.71838601]
|
||||
[0.68655456 0.11747908 0.28253033 0.4591127 0.68072161 0.59372982
|
||||
0.95343966 0.24780663 0.98740373 0.06808421]
|
||||
[0.99512017 0.14828178 0.02354386 0.90860768 0.891715 0.39039235
|
||||
0.48151166 0.43563433 0.52657934 0.73176319]
|
||||
[0.77030637 0.00676256 0.37454707 0.5076963 0.51937727 0.46065811
|
||||
0.65917558 0.72962885 0.99370678 0.92341148]
|
||||
[0.16292908 0.17214545 0.44995924 0.20367355 0.64885265 0.34225662
|
||||
0.4215795 0.27933134 0.02552966 0.62908496]
|
||||
[0.8084934 0.51364117 0.4937346 0.05296475 0.69247718 0.56783103
|
||||
0.85276538 0.52635761 0.96461948 0.67374815]
|
||||
[0.02137508 0.03177331 0.78186404 0.33096549 0.8423144 0.07745579
|
||||
0.4619526 0.61414743 0.38460453 0.51928402]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -914,13 +924,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.0018310257999764163
|
||||
4.092608577084595
|
||||
0.31555734196707536
|
||||
[[ 0.78671736 2.38337498 2.04657426]
|
||||
[ 2.38337498 8.33235647 6.05002471]
|
||||
[ 2.04657426 6.05002471 10.13152828]]
|
||||
[15.98413606 0.08227668 3.18418938]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07218473624441492
|
||||
4.346000154268618
|
||||
0.09048717285916912
|
||||
[[ 1.0974119 3.2131067 3.36880327]
|
||||
[ 3.2131067 10.51564682 9.75138064]
|
||||
[ 3.36880327 9.75138064 17.26527089]]
|
||||
[25.09487358 0.09070064 3.6927554 ]
|
||||
</pre></div>
|
||||
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|
||||
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||||
|
||||
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Week 39: Optimization and Gradient Methods
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Week 38: Logistic Regression and Optimization
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Week 39: Optimization and Gradient Methods
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||||
@@ -985,27 +995,27 @@ uncorrelated.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9841870203276504
|
||||
[[ 3.57492326 2.52888979 5.61382924 2.32419549 4.2986082 3.83718206
|
||||
4.7658599 4.76527062 8.55196383 8.05747369]
|
||||
[ 2.52888979 1.78892891 3.97120565 1.64412879 3.0408223 2.71441086
|
||||
3.37135473 3.37093787 6.04963309 5.69983227]
|
||||
[ 5.61382924 3.97120565 8.81559586 3.64976691 6.75025744 6.02566356
|
||||
7.48399942 7.48307405 13.42945319 12.65293772]
|
||||
[ 2.32419549 1.64412879 3.64976691 1.51104913 2.79469098 2.49470005
|
||||
3.09846933 3.09808622 5.55996153 5.23847441]
|
||||
[ 4.2986082 3.0408223 6.75025744 2.79469098 5.16879134 4.61395701
|
||||
5.73063053 5.72992196 10.28316949 9.68857788]
|
||||
[ 3.83718206 2.71441086 6.02566356 2.49470005 4.61395701 4.11868033
|
||||
5.11548661 5.1148541 9.1793417 8.64857542]
|
||||
[ 4.7658599 3.37135473 7.48399942 3.09846933 5.73063053 5.11548661
|
||||
6.35354073 6.35275513 11.40093324 10.74171049]
|
||||
[ 4.76527062 3.37093787 7.48307405 3.09808622 5.72992196 5.1148541
|
||||
6.35275513 6.35196964 11.39952356 10.74038232]
|
||||
[ 8.55196383 6.04963309 13.42945319 5.55996153 10.28316949 9.1793417
|
||||
11.40093324 11.39952356 20.4580854 19.2751616 ]
|
||||
[ 8.05747369 5.69983227 12.65293772 5.23847441 9.68857788 8.64857542
|
||||
10.74171049 10.74038232 19.2751616 18.16063661]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>3.613893902124586
|
||||
[[18.33217312 13.09829902 1.98271562 18.53534008 -0.88860399 18.12957454
|
||||
7.18043393 1.59698459 17.87186187 10.81979166]
|
||||
[13.09829902 9.35870701 1.41664613 13.24346138 -0.63490568 12.95354276
|
||||
5.13040489 1.14104212 12.76940759 7.73071831]
|
||||
[ 1.98271562 1.41664613 0.21444055 2.00468914 -0.09610694 1.96080358
|
||||
0.77659961 0.17272182 1.93293067 1.17021424]
|
||||
[18.53534008 13.24346138 2.00468914 18.74075864 -0.89845198 18.33049619
|
||||
7.26001134 1.61468323 18.0699274 10.93970238]
|
||||
[-0.88860399 -0.63490568 -0.09610694 -0.89845198 0.04307275 -0.87878356
|
||||
-0.3480527 -0.07740964 -0.86629161 -0.52446101]
|
||||
[18.12957454 12.95354276 1.96080358 18.33049619 -0.87878356 17.92921498
|
||||
7.10107914 1.57933547 17.67435043 10.7002164 ]
|
||||
[ 7.18043393 5.13040489 0.77659961 7.26001134 -0.3480527 7.10107914
|
||||
2.81246697 0.62551462 7.000137 4.23794815]
|
||||
[ 1.59698459 1.14104212 0.17272182 1.61468323 -0.07740964 1.57933547
|
||||
0.62551462 0.13911934 1.55688514 0.94255277]
|
||||
[17.87186187 12.76940759 1.93293067 18.0699274 -0.86629161 17.67435043
|
||||
7.000137 1.55688514 17.42310878 10.54811237]
|
||||
[10.81979166 7.73071831 1.17021424 10.93970238 -0.52446101 10.7002164
|
||||
4.23794815 0.94255277 10.54811237 6.38592549]]
|
||||
</pre></div>
|
||||
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|
||||
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|
||||
@@ -1273,15 +1283,15 @@ more practically oriented methods like the blocking technique.</p>
|
||||
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|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07950356694388497
|
||||
4.124228866018077
|
||||
0.3908470004999506
|
||||
1.2475908482537097 11.548432150659993 27.870704644539707
|
||||
3.6568686180915178 4.6156409232714415 13.395980256477532
|
||||
[[ 1.24759085 3.65686862 4.61564092]
|
||||
[ 3.65686862 11.54843215 13.39598026]
|
||||
[ 4.61564092 13.39598026 27.87070464]]
|
||||
[36.35957915 0.07241855 4.23472994]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0973900819831327
|
||||
4.559791959661649
|
||||
0.6333349473431832
|
||||
1.1064601390492845 11.271260217275557 17.072290639572326
|
||||
3.390334838933238 3.4951301940723654 11.033233504714921
|
||||
[[ 1.10646014 3.39033484 3.49513019]
|
||||
[ 3.39033484 11.27126022 11.0332335 ]
|
||||
[ 3.49513019 11.0332335 17.07229064]]
|
||||
[26.5020612 0.075885 2.8720648]
|
||||
</pre></div>
|
||||
</div>
|
||||
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|
||||
@@ -1611,7 +1621,7 @@ assumption for approximating <span class="math notranslate nohighlight">\(\sigma
|
||||
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|
||||
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|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.05577845931438246 1.0303586629618948
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.02214409916811925 1.073576975500551
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/statistics_188_1.png" src="_images/statistics_188_1.png" />
|
||||
|
||||
@@ -296,6 +296,16 @@ const thebe_selector_output = ".output, .cell_output"
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||||
Week 38: Logistic Regression and Optimization
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||||
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||||
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||||
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||||
@@ -296,6 +296,16 @@ const thebe_selector_output = ".output, .cell_output"
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||||
Week 38: Logistic Regression and Optimization
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Week 39: Optimization and Gradient Methods
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||||
@@ -1673,8 +1683,8 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
|
||||
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|
||||
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|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-1.24454968 1.12382443 0.67088558 1.12498355 1.0342028 -0.44563226
|
||||
0.14599499 0.07378525 0.03479236 -1.2976637 ]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.60588173 1.59884169 -1.56922102 -1.32068736 -0.21631786 0.37600869
|
||||
-0.14841322 -0.83655756 0.88809826 -0.85625134]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1899,26 +1909,26 @@ lowercase letters for vectors and uppercase letters for matrices)</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.50306335 0.66487438 0.75677341 0.01349244 0.2813829 0.80056922
|
||||
0.07974741 0.63046054 0.05098714 0.26479234]
|
||||
[0.17861414 0.3388112 0.30005983 0.35520169 0.5399913 0.51709529
|
||||
0.36339156 0.71582784 0.34568909 0.23164401]
|
||||
[0.11922031 0.771128 0.20051449 0.07890044 0.96866031 0.34346829
|
||||
0.5116375 0.52732966 0.80637385 0.69435454]
|
||||
[0.94291287 0.29238145 0.84711297 0.22849742 0.56967917 0.1636508
|
||||
0.15833751 0.84254917 0.05068486 0.54057582]
|
||||
[0.17856374 0.71524686 0.66498292 0.00256622 0.72427854 0.50667812
|
||||
0.0894015 0.22688898 0.54873252 0.31727523]
|
||||
[0.73578772 0.81479491 0.45620975 0.2662452 0.47757553 0.64322974
|
||||
0.54921401 0.70630967 0.51136852 0.59683811]
|
||||
[0.37837864 0.71860732 0.35320952 0.67495943 0.16188604 0.41925189
|
||||
0.28956161 0.06685171 0.75654448 0.28923 ]
|
||||
[0.91099021 0.8387133 0.18277213 0.40418675 0.7249499 0.46415522
|
||||
0.35018806 0.87148597 0.94141801 0.50911289]
|
||||
[0.86066395 0.12235593 0.82418352 0.57881465 0.82559478 0.96826039
|
||||
0.291056 0.41675053 0.06430789 0.96432396]
|
||||
[0.91270333 0.64362404 0.18816387 0.81318307 0.47989224 0.20375464
|
||||
0.33145794 0.92192012 0.33596404 0.18085537]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.32641434 0.35731585 0.64796751 0.41146753 0.67561021 0.53312817
|
||||
0.3910042 0.88157423 0.4576811 0.48004784]
|
||||
[0.70469324 0.28496213 0.84862355 0.6988905 0.95890587 0.19849513
|
||||
0.89058005 0.51546825 0.88289263 0.06926192]
|
||||
[0.38198866 0.33000573 0.80740939 0.54935794 0.38934047 0.87740526
|
||||
0.45053025 0.27231287 0.7070883 0.7989356 ]
|
||||
[0.4198932 0.3727791 0.95400323 0.86459987 0.2666905 0.13564988
|
||||
0.97498674 0.9450635 0.6383903 0.57803254]
|
||||
[0.13896095 0.13663125 0.68826552 0.13729154 0.91672129 0.08266769
|
||||
0.88639567 0.16407038 0.36353321 0.81007381]
|
||||
[0.31849289 0.68735473 0.1767857 0.42873361 0.44454123 0.21333766
|
||||
0.94285762 0.72710494 0.37153115 0.21070843]
|
||||
[0.11930916 0.28021598 0.69566966 0.98770503 0.88653291 0.82161167
|
||||
0.90114639 0.7127128 0.97486336 0.26152075]
|
||||
[0.55386681 0.37919989 0.57468142 0.35980374 0.7150195 0.70499955
|
||||
0.9647801 0.63142399 0.97512176 0.97570392]
|
||||
[0.24613581 0.62573269 0.41487642 0.42095725 0.51447004 0.41869784
|
||||
0.34483955 0.55582742 0.85711016 0.17739525]
|
||||
[0.89533642 0.03382942 0.918785 0.79718864 0.64361375 0.4843772
|
||||
0.33532886 0.13164176 0.63209435 0.39279291]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1973,13 +1983,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.1385510301651882
|
||||
4.344176915013831
|
||||
0.13134148011170077
|
||||
[[ 0.87981676 2.52698542 2.65591748]
|
||||
[ 2.52698542 8.29861395 7.76790092]
|
||||
[ 2.65591748 7.76790092 13.4831139 ]]
|
||||
[19.77845284 0.09028702 2.79280475]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.050315327923114654
|
||||
3.7539148284817965
|
||||
-0.09246293455466892
|
||||
[[ 0.90894281 2.8691787 2.58589719]
|
||||
[ 2.8691787 10.23481471 8.16535252]
|
||||
[ 2.58589719 8.16535252 12.44536331]]
|
||||
[20.33742926 0.08458591 3.16710567]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2204,7 +2214,7 @@ Name: Aragorn, dtype: object
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">AttributeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58840/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95519/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="ne">----> </span><span class="mi">6</span> <span class="n">new_hobbit</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'First Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Peregrin"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">7</span> <span class="s1">'Last Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Took"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="s1">'Place of birth'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Shire"</span><span class="p">],</span>
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1641,7 +1651,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9969513794144311
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9952505213910134
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1658,7 +1668,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.007658477904313023
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.008753288788081405
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1673,23 +1683,31 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.00053122 0.03115122 0.00789262 0.02218076 0.00573727 0.00557893
|
||||
0.00099778 0.01234 0.03960002 0.03596557 0.0134113 0.00556946
|
||||
0.00136125 0.10719554 0.02754248 0.01409478 0.01760144 0.01032533
|
||||
0.01241284 0.01039879 0.00100913 0.02944152 0.00512599 0.00747773
|
||||
0.06260611 0.0231353 0.01624447 0.02923006 0.0046544 0.07332248
|
||||
0.02338085 0.02920675 0.02286267 0.04353549 0.00569512 0.02664408
|
||||
0.01098247 0.02156565 0.03529801 0.00507531 0.00554202 0.05141614
|
||||
0.02031987 0.01244297 0.01551724 0.00174738 0.01044475 0.01161645
|
||||
0.02622039 0.03285784 0.00522055 0.00687309 0.0195302 0.04101344
|
||||
0.00816675 0.0206033 0.04046513 0.02189863 0.06777772 0.04832356
|
||||
0.00114855 0.08660891 0.00586355 0.00625051 0.00939407 0.00108471
|
||||
0.03948301 0.02527621 0.03205795 0.11042239 0.02594314 0.05176711
|
||||
0.03396658 0.00889475 0.02632742 0.02502325 0.01266999 0.00455966
|
||||
0.03853313 0.01543076 0.00617221 0.00552462 0.01573062 0.01035006
|
||||
0.00162921 0.00974758 0.00812487 0.01881237 0.06690071 0.01499192
|
||||
0.04652794 0.04061345 0.04495752 0.00566707 0.01006984 0.00519717
|
||||
0.00151416 0.03214829 0.00891702 0.01844822]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[8.90304177e-02 3.21655059e-02 1.15924557e-02 1.83823317e-02
|
||||
8.19559737e-03 1.66018725e-02 1.79135536e-03 1.03313259e-01
|
||||
7.69182892e-04 1.29306584e-02 1.21565007e-02 2.83463634e-03
|
||||
3.03538673e-02 2.37415625e-02 1.56790195e-02 9.03400724e-03
|
||||
1.35613536e-02 5.35506347e-02 1.01123792e-02 4.10604579e-02
|
||||
2.63898112e-02 1.94766419e-02 3.81425129e-02 3.27482829e-02
|
||||
5.12829994e-03 6.02901273e-03 8.26321660e-02 4.04504728e-02
|
||||
2.20601797e-02 4.62113349e-03 9.03476611e-04 4.87494456e-02
|
||||
3.82060913e-03 2.53729411e-02 2.38612299e-02 1.59355752e-02
|
||||
3.60160003e-03 1.65738717e-02 2.98947674e-02 5.18501900e-03
|
||||
9.36303682e-03 4.81218742e-02 1.49392067e-02 4.88551766e-03
|
||||
2.17643975e-02 2.20608548e-04 1.90135464e-02 2.74291603e-02
|
||||
1.23344210e-02 6.03309191e-03 1.57252451e-02 9.02612988e-03
|
||||
3.32084559e-02 3.76692036e-03 2.87169607e-02 4.85551266e-02
|
||||
1.48826894e-02 6.41842093e-04 1.89017198e-02 3.49584063e-02
|
||||
1.77652198e-02 6.38298234e-03 1.05034088e-03 1.99753321e-02
|
||||
5.52031552e-03 8.22217237e-03 6.86192682e-02 8.40354798e-03
|
||||
1.29491144e-02 7.44658658e-03 1.00731392e-02 9.52284329e-02
|
||||
1.51437058e-02 2.00002585e-05 2.37700967e-02 1.95166920e-02
|
||||
4.82376174e-02 3.73986200e-02 4.84707251e-02 8.76887316e-02
|
||||
2.74724414e-02 5.14825560e-03 1.26254957e-02 2.81042619e-02
|
||||
2.11265643e-02 2.52301447e-03 3.13819592e-02 2.93900569e-02
|
||||
3.65720152e-02 1.02850506e-02 4.85945208e-02 2.79870689e-02
|
||||
3.12846660e-02 6.17869861e-02 9.09590269e-03 1.11715109e-02
|
||||
3.62863106e-02 1.21277816e-02 9.05665429e-03 4.85293303e-02]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1758,15 +1776,15 @@ but now splitting the data into a training set and a test set.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.97243946 0.15593478 4.54011398 0.56342158 -0.19299283]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 2.05054319 -0.48521055 6.95338273 -2.63619709 1.0524497 ]
|
||||
Training R2
|
||||
0.9948998579029953
|
||||
0.9959308805732706
|
||||
Training MSE
|
||||
0.009396472959497925
|
||||
0.009211602191395454
|
||||
Test R2
|
||||
0.9951059931014423
|
||||
0.9955318336036834
|
||||
Test MSE
|
||||
0.010612904886352397
|
||||
0.011818646101922625
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2430,7 +2448,9 @@ the aims is to reproduce Figure 2.11 of <a class="reference external" href="http
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>MSE before scaling: 0.00
|
||||
R2 score before scaling 1.00
|
||||
Feature min values before scaling:
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Feature min values before scaling:
|
||||
[1.00000000e+00 6.97906022e-03 2.43639284e-03 4.87072815e-05
|
||||
1.70037324e-05 5.93601008e-06 3.39931051e-07 1.18670072e-07
|
||||
4.14277718e-08 1.44624525e-08 2.37239927e-09 8.28205578e-10
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1629,7 +1639,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
99.8244 15.0449 99.8227 0.150527
|
||||
99.8485 15.0562 99.8488 0.149353
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1849,7 +1859,9 @@ Error: 0.08426840630693411
|
||||
Bias^2: 0.0796891867672603
|
||||
Var: 0.004579219539673834
|
||||
0.08426840630693411 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
|
||||
Polynomial degree: 2
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 2
|
||||
Error: 0.10398646080125035
|
||||
Bias^2: 0.1007711427354898
|
||||
Var: 0.0032153180657605116
|
||||
@@ -1864,14 +1876,14 @@ Error: 0.06844519414009445
|
||||
Bias^2: 0.06453579006728324
|
||||
Var: 0.003909404072811226
|
||||
0.06844519414009445 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
0.05227921801205686 >= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
|
||||
Polynomial degree: 6
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
@@ -1881,7 +1893,9 @@ Error: 0.02760977349102253
|
||||
Bias^2: 0.022999498260366312
|
||||
Var: 0.004610275230656212
|
||||
0.02760977349102253 >= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525
|
||||
Polynomial degree: 8
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 8
|
||||
Error: 0.017355848195593347
|
||||
Bias^2: 0.010331721306655127
|
||||
Var: 0.007024126888938232
|
||||
@@ -1896,17 +1910,14 @@ Error: 0.021592704588025025
|
||||
Bias^2: 0.010516485576645508
|
||||
Var: 0.011076219011379514
|
||||
0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree:
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 11
|
||||
Polynomial degree: 11
|
||||
Error: 0.07160048164233104
|
||||
Bias^2: 0.014436800088904942
|
||||
Var: 0.05716368155342608
|
||||
0.07160048164233104 >= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
|
||||
Polynomial degree: 12
|
||||
</pre></div>
|
||||
</div>
|
||||
<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
|
||||
@@ -1918,7 +1929,7 @@ Var: 0.20867052175034223
|
||||
0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week37_139_4.png" src="_images/week37_139_4.png" />
|
||||
<img alt="_images/week37_139_5.png" src="_images/week37_139_5.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2349,9 +2360,9 @@ Mean squared error on training data: 0.00063866
|
||||
Mean squared error on test data: 3099.60342978
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58862/626635268.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_95542/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58862/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95542/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2436,7 +2447,7 @@ Mean squared error on test data: 3099.60342978
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58862/3817475779.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_95542/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
|
||||
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 1 on Machine Learning, deadline October 7 (midnight), 2024" href="project1.html" />
|
||||
<link rel="next" title="Exercises week 39" href="exercisesweek39.html" />
|
||||
<link rel="prev" title="Exercises week 38" href="exercisesweek38.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 38: Logistic Regression and Optimization
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek39.html">
|
||||
Exercises week 39
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week39.html">
|
||||
Week 39: Optimization and Gradient Methods
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -2691,10 +2701,10 @@ cross-validation (LOOCV).</p>
|
||||
<p class="prev-next-title">Exercises week 38</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="project1.html" title="next page">
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<a class='right-next' id="next-link" href="exercisesweek39.html" title="next page">
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<div class="prev-next-info">
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<p class="prev-next-subtitle">next</p>
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||||
<p class="prev-next-title">Project 1 on Machine Learning, deadline October 7 (midnight), 2024</p>
|
||||
<p class="prev-next-title">Exercises week 39</p>
|
||||
</div>
|
||||
<i class="fas fa-angle-right"></i>
|
||||
</a>
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
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@@ -2981,22 +2981,16 @@
|
||||
"Cell \u001b[0;32mIn[9], line 143\u001b[0m\n\u001b[1;32m 140\u001b[0m num_iter \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m250\u001b[39m\n\u001b[1;32m 141\u001b[0m lmb \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.01\u001b[39m\n\u001b[0;32m--> 143\u001b[0m P \u001b[38;5;241m=\u001b[39m \u001b[43msolve_pde_deep_neural_network\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_hidden_neurons\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_iter\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlmb\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 145\u001b[0m \u001b[38;5;66;03m## Store the results\u001b[39;00m\n\u001b[1;32m 146\u001b[0m g_dnn_ag \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((Nx, Nt))\n",
|
||||
"Cell \u001b[0;32mIn[9], line 120\u001b[0m, in \u001b[0;36msolve_pde_deep_neural_network\u001b[0;34m(x, t, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m 118\u001b[0m \u001b[38;5;66;03m# Let the update be done num_iter times\u001b[39;00m\n\u001b[1;32m 119\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_iter):\n\u001b[0;32m--> 120\u001b[0m cost_grad \u001b[38;5;241m=\u001b[39m \u001b[43mcost_function_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mP\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 122\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m l \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(N_hidden\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m 123\u001b[0m P[l] \u001b[38;5;241m=\u001b[39m P[l] \u001b[38;5;241m-\u001b[39m lmb \u001b[38;5;241m*\u001b[39m cost_grad[l]\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:28\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m 23\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 24\u001b[0m \u001b[38;5;124;03m Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m 25\u001b[0m \u001b[38;5;124;03m positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m 26\u001b[0m \u001b[38;5;124;03m arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m 27\u001b[0m \u001b[38;5;124;03m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 28\u001b[0m vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 29\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 31\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m 9\u001b[0m start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m end_value, end_node \u001b[38;5;241m=\u001b[39m \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m 9\u001b[0m start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 14\u001b[0m subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"Cell \u001b[0;32mIn[9], line 80\u001b[0m, in \u001b[0;36mcost_function\u001b[0;34m(P, x, t)\u001b[0m\n\u001b[1;32m 78\u001b[0m g_t \u001b[38;5;241m=\u001b[39m g_trial(point,P)\n\u001b[1;32m 79\u001b[0m g_t_jacobian \u001b[38;5;241m=\u001b[39m g_t_jacobian_func(point,P)\n\u001b[0;32m---> 80\u001b[0m g_t_hessian \u001b[38;5;241m=\u001b[39m \u001b[43mg_t_hessian_func\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpoint\u001b[49m\u001b[43m,\u001b[49m\u001b[43mP\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 82\u001b[0m g_t_dt \u001b[38;5;241m=\u001b[39m g_t_jacobian[\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 83\u001b[0m g_t_d2x \u001b[38;5;241m=\u001b[39m g_t_hessian[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m0\u001b[39m]\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:81\u001b[0m, in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 79\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhessian\u001b[39m(fun, x):\n\u001b[1;32m 80\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mReturns a function that computes the exact Hessian.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m---> 81\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:64\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 62\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m 63\u001b[0m grads \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(vjp, ans_vspace\u001b[38;5;241m.\u001b[39mstandard_basis())\n\u001b[0;32m---> 64\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mreshape(\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgrads\u001b[49m\u001b[43m)\u001b[49m, jacobian_shape)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:32\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 31\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m---> 32\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvspace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mones\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp.<locals>.vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m 20\u001b[0m outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m 23\u001b[0m outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m 65\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m 66\u001b[0m vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m 68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m 69\u001b[0m argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:660\u001b[0m, in \u001b[0;36munbroadcast_f.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 658\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21munbroadcast_f\u001b[39m(target, f):\n\u001b[1;32m 659\u001b[0m target_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(target)\n\u001b[0;32m--> 660\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43munbroadcast\u001b[49m\u001b[43m(\u001b[49m\u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtarget_meta\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:651\u001b[0m, in \u001b[0;36munbroadcast\u001b[0;34m(x, target_meta, broadcast_idx)\u001b[0m\n\u001b[1;32m 649\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m anp\u001b[38;5;241m.\u001b[39mndim(x) \u001b[38;5;241m>\u001b[39m target_ndim:\n\u001b[1;32m 650\u001b[0m x \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msum(x, axis\u001b[38;5;241m=\u001b[39mbroadcast_idx)\n\u001b[0;32m--> 651\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m axis, size \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28;43menumerate\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mtarget_shape\u001b[49m\u001b[43m)\u001b[49m:\n\u001b[1;32m 652\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m size \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m 653\u001b[0m x \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msum(x, axis\u001b[38;5;241m=\u001b[39maxis, keepdims\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:653\u001b[0m, in \u001b[0;36munbroadcast\u001b[0;34m(x, target_meta, broadcast_idx)\u001b[0m\n\u001b[1;32m 651\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m axis, size \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(target_shape):\n\u001b[1;32m 652\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m size \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[0;32m--> 653\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msum\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkeepdims\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m 654\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m anp\u001b[38;5;241m.\u001b[39miscomplexobj(x) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m target_iscomplex:\n\u001b[1;32m 655\u001b[0m x \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mreal(x)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48\u001b[0m, in \u001b[0;36mprimitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 46\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m 47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 48\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m<__array_function__ internals>:180\u001b[0m, in \u001b[0;36msum\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:2296\u001b[0m, in \u001b[0;36msum\u001b[0;34m(a, axis, dtype, out, keepdims, initial, where)\u001b[0m\n\u001b[1;32m 2293\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m out\n\u001b[1;32m 2294\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m res\n\u001b[0;32m-> 2296\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_wrapreduction\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43madd\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43msum\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkeepdims\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mkeepdims\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 2297\u001b[0m \u001b[43m \u001b[49m\u001b[43minitial\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minitial\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwhere\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mwhere\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:86\u001b[0m, in \u001b[0;36m_wrapreduction\u001b[0;34m(obj, ufunc, method, axis, dtype, out, **kwargs)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 84\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m reduction(axis\u001b[38;5;241m=\u001b[39maxis, out\u001b[38;5;241m=\u001b[39mout, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mpasskwargs)\n\u001b[0;32m---> 86\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mufunc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreduce\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobj\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mpasskwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
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"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
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]
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@@ -1798,10 +1798,10 @@
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"name": "stdout",
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"text": [
|
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"-0.07978850553011713\n",
|
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"3.8232102961414203\n",
|
||||
"[[ 1.25705685 3.70704566]\n",
|
||||
" [ 3.70704566 12.1664372 ]]\n"
|
||||
"-0.024792624800382218\n",
|
||||
"3.9225384545636204\n",
|
||||
"[[0.94623184 2.84401886]\n",
|
||||
" [2.84401886 9.4477214 ]]\n"
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]
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}
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],
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@@ -1845,10 +1845,10 @@
|
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
||||
"0.08931169286872433\n",
|
||||
"2.047447724189861\n",
|
||||
"[[1. 0.66729685]\n",
|
||||
" [0.66729685 1. ]]\n"
|
||||
"0.08536248571780691\n",
|
||||
"1.8207274870895702\n",
|
||||
"[[1. 0.74900488]\n",
|
||||
" [0.74900488 1. ]]\n"
|
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]
|
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}
|
||||
],
|
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@@ -1905,30 +1905,36 @@
|
||||
"name": "stdout",
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"output_type": "stream",
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"text": [
|
||||
"[[ 2.37582891 5.4242743 ]\n",
|
||||
" [-0.81925302 -3.60052901]\n",
|
||||
" [ 0.37467515 3.16158074]\n",
|
||||
" [-0.40478305 -2.22601408]\n",
|
||||
" [-0.0776532 -1.70594608]\n",
|
||||
" [-0.99434472 -2.2026985 ]\n",
|
||||
" [ 0.71376303 2.77725472]\n",
|
||||
" [ 0.94637206 2.69303453]\n",
|
||||
" [-0.19791352 0.93366198]\n",
|
||||
" [-1.91669165 -5.2546186 ]]\n",
|
||||
"[[ 1.10115017 1.66431407]\n",
|
||||
" [ 0.12043521 1.32305911]\n",
|
||||
" [-1.30023144 -3.36154104]\n",
|
||||
" [-0.25200841 -1.11277166]\n",
|
||||
" [-1.55102329 -4.20158083]\n",
|
||||
" [ 0.72770687 0.97206657]\n",
|
||||
" [ 0.76533281 2.10747579]\n",
|
||||
" [-0.20666447 0.79623487]\n",
|
||||
" [-0.63919355 -2.48490503]\n",
|
||||
" [ 1.23449607 4.29764815]]\n"
|
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]
|
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},
|
||||
{
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||||
"name": "stdout",
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"output_type": "stream",
|
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"metadata": {
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},
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||||
"source": [
|
||||
"# Exercises week 39\n",
|
||||
"**September 23-27, 2024**\n",
|
||||
"\n",
|
||||
"Date: **Deadline is Friday September 27 at midnight**"
|
||||
]
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},
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{
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"metadata": {
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},
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||||
"source": [
|
||||
"## Overarching aims of the exercises this week\n",
|
||||
"\n",
|
||||
"The aim of the exercises this week is to aid you in getting started\n",
|
||||
"with writing the report. This will be discussed during the lab\n",
|
||||
"sessions as well. \n",
|
||||
"\n",
|
||||
"A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
|
||||
"\n",
|
||||
"Similarly, an example of an earlier project can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf>\n",
|
||||
"\n",
|
||||
"Your task this week is to\n",
|
||||
"1. Write an abstract for your project\n",
|
||||
"\n",
|
||||
"2. Write an introduction\n",
|
||||
"\n",
|
||||
"3. Include references\n",
|
||||
"\n",
|
||||
"A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report."
|
||||
]
|
||||
}
|
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],
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|
||||
" 0.28956161 0.06685171 0.75654448 0.28923 ]\n",
|
||||
" [0.91099021 0.8387133 0.18277213 0.40418675 0.7249499 0.46415522\n",
|
||||
" 0.35018806 0.87148597 0.94141801 0.50911289]\n",
|
||||
" [0.86066395 0.12235593 0.82418352 0.57881465 0.82559478 0.96826039\n",
|
||||
" 0.291056 0.41675053 0.06430789 0.96432396]\n",
|
||||
" [0.91270333 0.64362404 0.18816387 0.81318307 0.47989224 0.20375464\n",
|
||||
" 0.33145794 0.92192012 0.33596404 0.18085537]]\n"
|
||||
"[[0.32641434 0.35731585 0.64796751 0.41146753 0.67561021 0.53312817\n",
|
||||
" 0.3910042 0.88157423 0.4576811 0.48004784]\n",
|
||||
" [0.70469324 0.28496213 0.84862355 0.6988905 0.95890587 0.19849513\n",
|
||||
" 0.89058005 0.51546825 0.88289263 0.06926192]\n",
|
||||
" [0.38198866 0.33000573 0.80740939 0.54935794 0.38934047 0.87740526\n",
|
||||
" 0.45053025 0.27231287 0.7070883 0.7989356 ]\n",
|
||||
" [0.4198932 0.3727791 0.95400323 0.86459987 0.2666905 0.13564988\n",
|
||||
" 0.97498674 0.9450635 0.6383903 0.57803254]\n",
|
||||
" [0.13896095 0.13663125 0.68826552 0.13729154 0.91672129 0.08266769\n",
|
||||
" 0.88639567 0.16407038 0.36353321 0.81007381]\n",
|
||||
" [0.31849289 0.68735473 0.1767857 0.42873361 0.44454123 0.21333766\n",
|
||||
" 0.94285762 0.72710494 0.37153115 0.21070843]\n",
|
||||
" [0.11930916 0.28021598 0.69566966 0.98770503 0.88653291 0.82161167\n",
|
||||
" 0.90114639 0.7127128 0.97486336 0.26152075]\n",
|
||||
" [0.55386681 0.37919989 0.57468142 0.35980374 0.7150195 0.70499955\n",
|
||||
" 0.9647801 0.63142399 0.97512176 0.97570392]\n",
|
||||
" [0.24613581 0.62573269 0.41487642 0.42095725 0.51447004 0.41869784\n",
|
||||
" 0.34483955 0.55582742 0.85711016 0.17739525]\n",
|
||||
" [0.89533642 0.03382942 0.918785 0.79718864 0.64361375 0.4843772\n",
|
||||
" 0.33532886 0.13164176 0.63209435 0.39279291]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1446,13 +1446,13 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.1385510301651882\n",
|
||||
"4.344176915013831\n",
|
||||
"0.13134148011170077\n",
|
||||
"[[ 0.87981676 2.52698542 2.65591748]\n",
|
||||
" [ 2.52698542 8.29861395 7.76790092]\n",
|
||||
" [ 2.65591748 7.76790092 13.4831139 ]]\n",
|
||||
"[19.77845284 0.09028702 2.79280475]\n"
|
||||
"-0.050315327923114654\n",
|
||||
"3.7539148284817965\n",
|
||||
"-0.09246293455466892\n",
|
||||
"[[ 0.90894281 2.8691787 2.58589719]\n",
|
||||
" [ 2.8691787 10.23481471 8.16535252]\n",
|
||||
" [ 2.58589719 8.16535252 12.44536331]]\n",
|
||||
"[20.33742926 0.08458591 3.16710567]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1808,7 +1808,7 @@
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58840/1326197715.py\u001b[0m in \u001b[0;36m?\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m new_hobbit = {'First Name': [\"Peregrin\"],\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0;34m'Last Name'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m\"Took\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;34m'Place of birth'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m\"Shire\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m'Date of Birth T.A.'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m2990\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_95519/1326197715.py\u001b[0m in \u001b[0;36m?\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m new_hobbit = {'First Name': [\"Peregrin\"],\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0;34m'Last Name'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m\"Took\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;34m'Place of birth'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m\"Shire\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m'Date of Birth T.A.'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m2990\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m?\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m 6200\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_accessors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6201\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6202\u001b[0m ):\n\u001b[1;32m 6203\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 6204\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||
"\u001b[0;31mAttributeError\u001b[0m: 'DataFrame' object has no attribute 'append'"
|
||||
]
|
||||
|
||||
@@ -1533,7 +1533,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.9969513794144311\n"
|
||||
"0.9952505213910134\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1564,7 +1564,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.007658477904313023\n"
|
||||
"0.008753288788081405\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1599,23 +1599,31 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[0.00053122 0.03115122 0.00789262 0.02218076 0.00573727 0.00557893\n",
|
||||
" 0.00099778 0.01234 0.03960002 0.03596557 0.0134113 0.00556946\n",
|
||||
" 0.00136125 0.10719554 0.02754248 0.01409478 0.01760144 0.01032533\n",
|
||||
" 0.01241284 0.01039879 0.00100913 0.02944152 0.00512599 0.00747773\n",
|
||||
" 0.06260611 0.0231353 0.01624447 0.02923006 0.0046544 0.07332248\n",
|
||||
" 0.02338085 0.02920675 0.02286267 0.04353549 0.00569512 0.02664408\n",
|
||||
" 0.01098247 0.02156565 0.03529801 0.00507531 0.00554202 0.05141614\n",
|
||||
" 0.02031987 0.01244297 0.01551724 0.00174738 0.01044475 0.01161645\n",
|
||||
" 0.02622039 0.03285784 0.00522055 0.00687309 0.0195302 0.04101344\n",
|
||||
" 0.00816675 0.0206033 0.04046513 0.02189863 0.06777772 0.04832356\n",
|
||||
" 0.00114855 0.08660891 0.00586355 0.00625051 0.00939407 0.00108471\n",
|
||||
" 0.03948301 0.02527621 0.03205795 0.11042239 0.02594314 0.05176711\n",
|
||||
" 0.03396658 0.00889475 0.02632742 0.02502325 0.01266999 0.00455966\n",
|
||||
" 0.03853313 0.01543076 0.00617221 0.00552462 0.01573062 0.01035006\n",
|
||||
" 0.00162921 0.00974758 0.00812487 0.01881237 0.06690071 0.01499192\n",
|
||||
" 0.04652794 0.04061345 0.04495752 0.00566707 0.01006984 0.00519717\n",
|
||||
" 0.00151416 0.03214829 0.00891702 0.01844822]\n"
|
||||
"[8.90304177e-02 3.21655059e-02 1.15924557e-02 1.83823317e-02\n",
|
||||
" 8.19559737e-03 1.66018725e-02 1.79135536e-03 1.03313259e-01\n",
|
||||
" 7.69182892e-04 1.29306584e-02 1.21565007e-02 2.83463634e-03\n",
|
||||
" 3.03538673e-02 2.37415625e-02 1.56790195e-02 9.03400724e-03\n",
|
||||
" 1.35613536e-02 5.35506347e-02 1.01123792e-02 4.10604579e-02\n",
|
||||
" 2.63898112e-02 1.94766419e-02 3.81425129e-02 3.27482829e-02\n",
|
||||
" 5.12829994e-03 6.02901273e-03 8.26321660e-02 4.04504728e-02\n",
|
||||
" 2.20601797e-02 4.62113349e-03 9.03476611e-04 4.87494456e-02\n",
|
||||
" 3.82060913e-03 2.53729411e-02 2.38612299e-02 1.59355752e-02\n",
|
||||
" 3.60160003e-03 1.65738717e-02 2.98947674e-02 5.18501900e-03\n",
|
||||
" 9.36303682e-03 4.81218742e-02 1.49392067e-02 4.88551766e-03\n",
|
||||
" 2.17643975e-02 2.20608548e-04 1.90135464e-02 2.74291603e-02\n",
|
||||
" 1.23344210e-02 6.03309191e-03 1.57252451e-02 9.02612988e-03\n",
|
||||
" 3.32084559e-02 3.76692036e-03 2.87169607e-02 4.85551266e-02\n",
|
||||
" 1.48826894e-02 6.41842093e-04 1.89017198e-02 3.49584063e-02\n",
|
||||
" 1.77652198e-02 6.38298234e-03 1.05034088e-03 1.99753321e-02\n",
|
||||
" 5.52031552e-03 8.22217237e-03 6.86192682e-02 8.40354798e-03\n",
|
||||
" 1.29491144e-02 7.44658658e-03 1.00731392e-02 9.52284329e-02\n",
|
||||
" 1.51437058e-02 2.00002585e-05 2.37700967e-02 1.95166920e-02\n",
|
||||
" 4.82376174e-02 3.73986200e-02 4.84707251e-02 8.76887316e-02\n",
|
||||
" 2.74724414e-02 5.14825560e-03 1.26254957e-02 2.81042619e-02\n",
|
||||
" 2.11265643e-02 2.52301447e-03 3.13819592e-02 2.93900569e-02\n",
|
||||
" 3.65720152e-02 1.02850506e-02 4.85945208e-02 2.79870689e-02\n",
|
||||
" 3.12846660e-02 6.17869861e-02 9.09590269e-03 1.11715109e-02\n",
|
||||
" 3.62863106e-02 1.21277816e-02 9.05665429e-03 4.85293303e-02]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1669,15 +1677,15 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[ 1.97243946 0.15593478 4.54011398 0.56342158 -0.19299283]\n",
|
||||
"[ 2.05054319 -0.48521055 6.95338273 -2.63619709 1.0524497 ]\n",
|
||||
"Training R2\n",
|
||||
"0.9948998579029953\n",
|
||||
"0.9959308805732706\n",
|
||||
"Training MSE\n",
|
||||
"0.009396472959497925\n",
|
||||
"0.009211602191395454\n",
|
||||
"Test R2\n",
|
||||
"0.9951059931014423\n",
|
||||
"0.9955318336036834\n",
|
||||
"Test MSE\n",
|
||||
"0.010612904886352397\n"
|
||||
"0.011818646101922625\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2549,7 +2557,13 @@
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"MSE before scaling: 0.00\n",
|
||||
"R2 score before scaling 1.00\n",
|
||||
"R2 score before scaling 1.00\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Feature min values before scaling:\n",
|
||||
" [1.00000000e+00 6.97906022e-03 2.43639284e-03 4.87072815e-05\n",
|
||||
" 1.70037324e-05 5.93601008e-06 3.39931051e-07 1.18670072e-07\n",
|
||||
|
||||
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Load Diff
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Load Diff
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Reference in New Issue
Block a user