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Morten Hjorth-Jensen
2024-11-25 08:12:27 +01:00
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commit c8f2aa3dc1
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@@ -257,6 +257,9 @@
<li class="toctree-l1"><a class="reference internal" href="week47.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek47.html">Exercise week 47</a></li>
<li class="toctree-l1"><a class="reference internal" href="week48.html">Week 48: Gradient boosting and summary of course</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek48.html">Exercises week 48</a></li>
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
<ul class="nav bd-sidenav">
@@ -617,10 +620,10 @@ 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>-0.08913527419249101
3.7127415072708665
[[ 1.13025431 3.39215451]
[ 3.39215451 11.15061293]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.02745698767039481
3.9527157086177156
[[0.80249705 2.35440603]
[2.35440603 7.83541057]]
</pre></div>
</div>
</div>
@@ -660,10 +663,10 @@ 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>0.09335279187105122
2.2108106787032815
[[1. 0.66771869]
[0.66771869 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07408022521552643
1.9519435372439522
[[1. 0.56323995]
[0.56323995 1. ]]
</pre></div>
</div>
</div>
@@ -692,30 +695,30 @@ 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>[[ 0.35582913 0.96196912]
[ 0.20039135 1.07902642]
[-0.47708415 -1.39752266]
[-0.0118395 0.55664957]
[-0.18990703 1.30646904]
[ 0.22370063 -0.76173777]
[-0.25925579 -1.7132548 ]
[-0.56061802 -1.9921751 ]
[-1.14025916 -4.44655399]
[ 1.85904253 6.40713017]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.53340467 1.72530188]
[-0.56167889 -3.2544002 ]
[ 1.85988539 5.87145508]
[-1.23561281 -4.57354138]
[ 0.52739566 0.93489572]
[ 0.89775088 2.87036267]
[-0.71834014 -0.65667853]
[ 0.38699758 1.30537358]
[-1.48772565 -3.9664681 ]
[-0.20207669 -0.25630072]]
0 1
0 0.355829 0.961969
1 0.200391 1.079026
2 -0.477084 -1.397523
3 -0.011839 0.556650
4 -0.189907 1.306469
5 0.223701 -0.761738
6 -0.259256 -1.713255
7 -0.560618 -1.992175
8 -1.140259 -4.446554
9 1.859043 6.407130
0 0.533405 1.725302
1 -0.561679 -3.254400
2 1.859885 5.871455
3 -1.235613 -4.573541
4 0.527396 0.934896
5 0.897751 2.870363
6 -0.718340 -0.656679
7 0.386998 1.305374
8 -1.487726 -3.966468
9 -0.202077 -0.256301
0 1
0 1.000000 0.946278
1 0.946278 1.000000
0 1.000000 0.966262
1 0.966262 1.000000
</pre></div>
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@@ -772,37 +775,37 @@ 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 0.075894 0.073179 0.073456 0.072746 0.071970 0.064485 0.064123
2 0.0 0.073179 0.070833 0.070597 0.070031 0.069409 0.061930 0.061649
3 0.0 0.073456 0.070597 0.076555 0.075647 0.074674 0.070295 0.069812
4 0.0 0.072746 0.070031 0.075647 0.074821 0.073930 0.069398 0.068968
5 0.0 0.071970 0.069409 0.074674 0.073930 0.073126 0.068445 0.068069
6 0.0 0.064485 0.061930 0.070295 0.069398 0.068445 0.066551 0.066050
7 0.0 0.064123 0.061649 0.069812 0.068968 0.068069 0.066050 0.065589
8 0.0 0.063763 0.061372 0.069330 0.068539 0.067694 0.065550 0.065128
9 0.0 0.063403 0.061097 0.068844 0.068107 0.067318 0.065047 0.064664
10 0.0 0.055942 0.053732 0.062913 0.062085 0.061210 0.060946 0.060463
11 0.0 0.055680 0.053525 0.062569 0.061780 0.060945 0.060582 0.060130
12 0.0 0.055429 0.053330 0.062237 0.061487 0.060692 0.060229 0.059808
13 0.0 0.055190 0.053147 0.061915 0.061205 0.060449 0.059887 0.059497
14 0.0 0.054960 0.052974 0.061603 0.060933 0.060217 0.059554 0.059195
1 0.0 0.073438 0.077471 0.075458 0.076186 0.076594 0.069080 0.068939
2 0.0 0.077471 0.083242 0.080919 0.082408 0.083412 0.074516 0.074729
3 0.0 0.075458 0.080919 0.083069 0.084410 0.085279 0.079308 0.079408
4 0.0 0.076186 0.082408 0.084410 0.086139 0.087327 0.080792 0.081105
5 0.0 0.076594 0.083412 0.085279 0.087327 0.088786 0.081792 0.082290
6 0.0 0.069080 0.074516 0.079308 0.080792 0.081792 0.077847 0.078070
7 0.0 0.068939 0.074729 0.079408 0.081105 0.082290 0.078070 0.078429
8 0.0 0.068716 0.074791 0.079363 0.081242 0.082589 0.078134 0.078618
9 0.0 0.068441 0.074753 0.079219 0.081258 0.082750 0.078091 0.078687
10 0.0 0.061939 0.066921 0.073159 0.074603 0.075599 0.073240 0.073520
11 0.0 0.061580 0.066741 0.072883 0.074456 0.075571 0.073054 0.073431
12 0.0 0.061213 0.066524 0.072574 0.074264 0.075487 0.072829 0.073296
13 0.0 0.060849 0.066290 0.072252 0.074047 0.075371 0.072584 0.073135
14 0.0 0.060497 0.066053 0.071930 0.073822 0.075239 0.072334 0.072965
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.063763 0.063403 0.055942 0.055680 0.055429 0.055190 0.054960
2 0.061372 0.061097 0.053732 0.053525 0.053330 0.053147 0.052974
3 0.069330 0.068844 0.062913 0.062569 0.062237 0.061915 0.061603
4 0.068539 0.068107 0.062085 0.061780 0.061487 0.061205 0.060933
5 0.067694 0.067318 0.061210 0.060945 0.060692 0.060449 0.060217
6 0.065550 0.065047 0.060946 0.060582 0.060229 0.059887 0.059554
7 0.065128 0.064664 0.060463 0.060130 0.059808 0.059497 0.059195
8 0.064706 0.064282 0.059981 0.059679 0.059388 0.059108 0.058837
9 0.064282 0.063898 0.059497 0.059226 0.058967 0.058718 0.058478
10 0.059981 0.059497 0.056837 0.056475 0.056124 0.055783 0.055452
11 0.059679 0.059226 0.056475 0.056139 0.055814 0.055499 0.055194
12 0.059388 0.058967 0.056124 0.055814 0.055515 0.055226 0.054947
13 0.059108 0.058718 0.055783 0.055499 0.055226 0.054963 0.054709
14 0.058837 0.058478 0.055452 0.055194 0.054947 0.054709 0.054481
1 0.068716 0.068441 0.061939 0.061580 0.061213 0.060849 0.060497
2 0.074791 0.074753 0.066921 0.066741 0.066524 0.066290 0.066053
3 0.079363 0.079219 0.073159 0.072883 0.072574 0.072252 0.071930
4 0.081242 0.081258 0.074603 0.074456 0.074264 0.074047 0.073822
5 0.082589 0.082750 0.075599 0.075571 0.075487 0.075371 0.075239
6 0.078134 0.078091 0.073240 0.073054 0.072829 0.072584 0.072334
7 0.078618 0.078687 0.073520 0.073431 0.073296 0.073135 0.072965
8 0.078919 0.079094 0.073650 0.073652 0.073602 0.073523 0.073430
9 0.079094 0.079368 0.073677 0.073765 0.073796 0.073795 0.073777
10 0.073650 0.073677 0.069911 0.069801 0.069653 0.069484 0.069308
11 0.073652 0.073765 0.069801 0.069768 0.069692 0.069593 0.069484
12 0.073602 0.073796 0.069653 0.069692 0.069686 0.069654 0.069611
13 0.073523 0.073795 0.069484 0.069593 0.069654 0.069688 0.069709
14 0.073430 0.073777 0.069308 0.069484 0.069611 0.069709 0.069791
</pre></div>
</div>
</div>
@@ -991,10 +994,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
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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 1
0 3.946263 1.971035
1 1.971035 1.988524
[[3.94626291 1.97103474]
[1.97103474 1.98852413]]
0 4.066103 2.050297
1 2.050297 2.019626
[[4.06610301 2.0502966 ]
[2.0502966 2.01962561]]
</pre></div>
</div>
</div>
@@ -1021,11 +1024,11 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
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<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
[[3.94626291 1.97103474]
[1.97103474 1.98852413]]
[[4.06610301 2.0502966 ]
[2.0502966 2.01962561]]
</pre></div>
</div>
<img alt="_images/6ca0e6a8c6122c37cbb752b49917fd1e67a1de46298e8c2247a990d083fdb3c7.png" src="_images/6ca0e6a8c6122c37cbb752b49917fd1e67a1de46298e8c2247a990d083fdb3c7.png" />
<img alt="_images/6221ee55bb26dba5cef5540ef9967df02eb119abda11c5c5903f7762c8c9f763.png" src="_images/6221ee55bb26dba5cef5540ef9967df02eb119abda11c5c5903f7762c8c9f763.png" />
</div>
</div>
<p>Depending on the number of points <span class="math notranslate nohighlight">\(n\)</span>, we will get results that are close to the covariance values defined above.
@@ -1082,16 +1085,16 @@ questions.</p>
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<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
5.168112312789667
0.7666747242371026
5.3343122336302145
0.7514163800957537
First eigenvector
[0.84993979 0.52687982]
[0.85045481 0.5260481 ]
Second eigenvector
[-0.52687982 0.84993979]
[-0.5260481 0.85045481]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[0.84993979 0.52687982]
[0.85045481 0.5260481 ]
</pre></div>
</div>
</div>