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Morten Hjorth-Jensen
2024-10-19 09:58:39 +02:00
parent 2476609846
commit 9a699212fa
357 changed files with 36568 additions and 3216 deletions
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@@ -338,6 +338,11 @@ const thebe_selector_output = ".output, .cell_output"
Exercises Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week43.html">
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -756,10 +761,10 @@ 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>0.044338305845698256
4.255107903576545
[[0.88333467 2.64297976]
[2.64297976 8.95889379]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.1621766238509487
3.735490390687699
[[0.74336924 2.19036055]
[2.19036055 7.50414881]]
</pre></div>
</div>
</div>
@@ -799,10 +804,10 @@ 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>0.07412144024494684
1.73876416607927
[[1. 0.65003213]
[0.65003213 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07865450504129884
1.6463440100796987
[[1. 0.63797452]
[0.63797452 1. ]]
</pre></div>
</div>
</div>
@@ -831,32 +836,30 @@ 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>[[-0.30897153 -0.91624469]
[-0.22194497 -0.77632217]
[ 1.6025456 6.69899609]
[-0.81040897 -2.22480853]
[-1.11048466 -2.70090777]
[-1.00173182 -4.12190193]
[-0.28603828 -0.45183405]
[ 0.90909173 2.29758118]
[ 0.99446145 1.7129466 ]
[ 0.23348144 0.48249527]]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
0 -0.308972 -0.916245
1 -0.221945 -0.776322
2 1.602546 6.698996
3 -0.810409 -2.224809
4 -1.110485 -2.700908
5 -1.001732 -4.121902
6 -0.286038 -0.451834
7 0.909092 2.297581
8 0.994461 1.712947
9 0.233481 0.482495
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.00615047 -0.51495078]
[-1.23076025 -3.95226818]
[ 0.14038959 1.1457534 ]
[ 0.7408594 2.69734853]
[ 0.19517373 1.18571046]
[-0.04178558 -0.58598227]
[ 0.45796224 0.7947491 ]
[ 0.3351443 0.35268457]
[ 0.04648472 0.35436034]
[-0.63731768 -1.47740516]]
0 1
0 1.000000 0.957549
1 0.957549 1.000000
0 -0.006150 -0.514951
1 -1.230760 -3.952268
2 0.140390 1.145753
3 0.740859 2.697349
4 0.195174 1.185710
5 -0.041786 -0.585982
6 0.457962 0.794749
7 0.335144 0.352685
8 0.046485 0.354360
9 -0.637318 -1.477405
0 1
0 1.000000 0.954148
1 0.954148 1.000000
</pre></div>
</div>
</div>
@@ -913,37 +916,40 @@ 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 0.070975 0.074460 0.075880 0.075241 0.074296 0.070514 0.069132
2 0.0 0.074460 0.078958 0.080631 0.080403 0.079783 0.075446 0.074283
3 0.0 0.075880 0.080631 0.085807 0.085728 0.085268 0.082553 0.081410
4 0.0 0.075241 0.080403 0.085728 0.085980 0.085820 0.082940 0.082057
5 0.0 0.074296 0.079783 0.085268 0.085820 0.085937 0.082957 0.082318
6 0.0 0.070514 0.075446 0.082553 0.082940 0.082957 0.081342 0.080608
7 0.0 0.069132 0.074283 0.081410 0.082057 0.082318 0.080608 0.080103
8 0.0 0.067779 0.073115 0.080268 0.081151 0.081637 0.079855 0.079562
9 0.0 0.066483 0.071976 0.079161 0.080258 0.080950 0.079114 0.079017
10 0.0 0.063682 0.068499 0.076361 0.077091 0.077476 0.076586 0.076225
11 0.0 0.062352 0.067313 0.075129 0.076065 0.076647 0.075671 0.075501
12 0.0 0.061118 0.066207 0.073985 0.075109 0.075872 0.074824 0.074830
13 0.0 0.059979 0.065183 0.072932 0.074228 0.075157 0.074048 0.074216
14 0.0 0.058935 0.064242 0.071969 0.073423 0.074506 0.073344 0.073662
1 0.0 0.078267 0.080363 0.077060 0.080735 0.084346 0.068278 0.071704
2 0.0 0.080363 0.084687 0.077184 0.081702 0.086410 0.067314 0.071070
3 0.0 0.077060 0.077184 0.081107 0.083982 0.086548 0.074851 0.078039
4 0.0 0.080735 0.081702 0.083982 0.087340 0.090475 0.076894 0.080380
5 0.0 0.084346 0.086410 0.086548 0.090475 0.094304 0.078548 0.082355
6 0.0 0.068278 0.067314 0.074851 0.076894 0.078548 0.071058 0.073683
7 0.0 0.071704 0.071070 0.078039 0.080380 0.082355 0.073683 0.076547
8 0.0 0.075284 0.075083 0.081283 0.083968 0.086326 0.076306 0.079429
9 0.0 0.079000 0.079369 0.084535 0.087621 0.090437 0.078867 0.082274
10 0.0 0.059805 0.058347 0.067435 0.068873 0.069916 0.065387 0.067507
11 0.0 0.062733 0.061411 0.070367 0.072006 0.073253 0.067940 0.070248
12 0.0 0.065842 0.064698 0.073442 0.075310 0.076791 0.070595 0.073109
13 0.0 0.069136 0.068226 0.076654 0.078782 0.080535 0.073340 0.076079
14 0.0 0.072615 0.072013 0.079987 0.082412 0.084486 0.076154 0.079138
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.067779 0.066483 0.063682 0.062352 0.061118 0.059979 0.058935
2 0.073115 0.071976 0.068499 0.067313 0.066207 0.065183 0.064242
3 0.080268 0.079161 0.076361 0.075129 0.073985 0.072932 0.071969
4 0.081151 0.080258 0.077091 0.076065 0.075109 0.074228 0.073423
5 0.081637 0.080950 0.077476 0.076647 0.075872 0.075157 0.074506
6 0.079855 0.079114 0.076586 0.075671 0.074824 0.074048 0.073344
7 0.079562 0.079017 0.076225 0.075501 0.074830 0.074216 0.073662
8 0.079218 0.078855 0.075830 0.075284 0.074776 0.074314 0.073899
9 0.078855 0.078661 0.075429 0.075048 0.074693 0.074372 0.074087
10 0.075830 0.075429 0.073114 0.072518 0.071969 0.071471 0.071027
11 0.075284 0.075048 0.072518 0.072085 0.071687 0.071328 0.071012
12 0.074776 0.074693 0.071969 0.071687 0.071427 0.071197 0.071001
13 0.074314 0.074372 0.071471 0.071328 0.071197 0.071087 0.071001
14 0.073899 0.074087 0.071027 0.071012 0.071001 0.071001 0.071018
1 0.075284 0.079000 0.059805 0.062733 0.065842 0.069136 0.072615
2 0.075083 0.079369 0.058347 0.061411 0.064698 0.068226 0.072013
3 0.081283 0.084535 0.067435 0.070367 0.073442 0.076654 0.079987
4 0.083968 0.087621 0.068873 0.072006 0.075310 0.078782 0.082412
5 0.086326 0.090437 0.069916 0.073253 0.076791 0.080535 0.084486
6 0.076306 0.078867 0.065387 0.067940 0.070595 0.073340 0.076154
7 0.079429 0.082274 0.067507 0.070248 0.073109 0.076079 0.079138
8 0.082598 0.085762 0.069592 0.072533 0.075613 0.078825 0.082151
9 0.085762 0.089288 0.071587 0.074738 0.078051 0.081523 0.085141
10 0.069592 0.071587 0.061178 0.063336 0.065565 0.067851 0.070172
11 0.072533 0.074738 0.063336 0.065655 0.068057 0.070529 0.073050
12 0.075613 0.078051 0.065565 0.068057 0.070647 0.073320 0.076057
13 0.078825 0.081523 0.067851 0.070529 0.073320 0.076212 0.079184
14 0.082151 0.085141 0.070172 0.073050 0.076057 0.079184 0.082414
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
</pre></div>
</div>
</div>
@@ -1132,10 +1138,10 @@ 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 3.972024 1.967388
1 1.967388 1.961423
[[3.97202371 1.96738845]
[1.96738845 1.96142343]]
0 3.847343 1.919895
1 1.919895 1.934339
[[3.8473429 1.91989533]
[1.91989533 1.934339 ]]
</pre></div>
</div>
</div>
@@ -1162,8 +1168,8 @@ 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
[[3.97202371 1.96738845]
[1.96738845 1.96142343]]
[[3.8473429 1.91989533]
[1.91989533 1.934339 ]]
</pre></div>
</div>
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
@@ -1223,16 +1229,16 @@ 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
5.176077701534979
0.7573694380469245
5.035810431523915
0.7458714725617228
First eigenvector
[0.85294194 0.52200578]
[0.8502729 0.52634209]
Second eigenvector
[-0.52200578 0.85294194]
[-0.52634209 0.8502729 ]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[-0.85294194 -0.52200578]
[-0.8502729 -0.52634209]
</pre></div>
</div>
</div>
@@ -1456,16 +1462,16 @@ training set, then extracts the first two principal components. First we center
7 0.0 0.0 0.0 0.0 0.0
8 0.0 0.0 0.0 0.0 0.0
9 0.0 0.0 0.0 0.0 0.0
[[-1.5378811 -0.94639099]
[ 0.86145244 0.89288636]
[-0.00445655 0.81633628]
[ 0.07145103 -1.00433417]
[ 2.03707133 -0.48476997]
[ 0.72174172 -1.4557763 ]
[-0.55854694 1.60673226]
[ 1.6999536 0.43766686]
[-1.10405456 0.31718909]
[-2.18673098 -0.17953942]]
[[-1.5378811 0.94639099]
[ 0.86145244 -0.89288636]
[-0.00445655 -0.81633628]
[ 0.07145103 1.00433417]
[ 2.03707133 0.48476997]
[ 0.72174172 1.4557763 ]
[-0.55854694 -1.60673226]
[ 1.6999536 -0.43766686]
[-1.10405456 -0.31718909]
[-2.18673098 0.17953942]]
</pre></div>
</div>
</div>