lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

update

Browse Source
This commit is contained in:
Morten Hjorth-Jensen
2023-08-31 06:19:44 +02:00
parent e9bac09427
commit d05f791ff6
98 changed files with 3861 additions and 2496 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/chapter8.html
+97 -70
View File
@@ -242,6 +242,33 @@ const thebe_selector_output = ".output, .cell_output"
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Weekly material, notes and exercises
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek34.html">
Exercises week 34
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week34.html">
Week 34: Introduction to the course, Logistics and Practicalities
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek35.html">
Exercises week 35
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week35.html">
Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
</a>
</li>
</ul>
</div>
</nav> <!-- To handle the deprecated key -->
@@ -642,10 +669,10 @@ 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>0.046785461905835435
4.240670854503034
[[0.94986593 2.88137798]
[2.88137798 9.93586895]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.264540221699101
4.673457751724773
[[0.83632853 2.54078623]
[2.54078623 8.44021223]]
</pre></div>
</div>
</div>
@@ -685,10 +712,10 @@ 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>0.08271198519070039
1.7306310662842432
[[1. 0.58084359]
[0.58084359 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08374032367704139
1.7696835316227453
[[1. 0.66443521]
[0.66443521 1. ]]
</pre></div>
</div>
</div>
@@ -717,30 +744,30 @@ 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>[[-0.50488131 -2.2493023 ]
[-0.26115367 -1.92631966]
[-1.43556723 -2.99992698]
[ 0.64528459 2.57643113]
[-0.55273102 -2.09964817]
[ 0.31681097 1.26466619]
[-0.04673082 -0.56607416]
[ 1.53394148 5.38629412]
[ 0.15092012 -0.22014758]
[ 0.15410688 0.83402742]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.20708879 4.33201844]
[-0.3838783 -1.24125217]
[ 0.74722409 1.60194224]
[-0.04086326 0.37419664]
[ 0.62422045 2.05587489]
[ 1.75357263 5.63710438]
[-2.53968309 -7.28219089]
[-1.42054337 -4.90629812]
[-0.13019959 -0.83320794]
[ 0.18306165 0.26181254]]
0 1
0 -0.504881 -2.249302
1 -0.261154 -1.926320
2 -1.435567 -2.999927
3 0.645285 2.576431
4 -0.552731 -2.099648
5 0.316811 1.264666
6 -0.046731 -0.566074
7 1.533941 5.386294
8 0.150920 -0.220148
9 0.154107 0.834027
0 1
0 1.00000 0.95302
1 0.95302 1.00000
0 1.207089 4.332018
1 -0.383878 -1.241252
2 0.747224 1.601942
3 -0.040863 0.374197
4 0.624220 2.055875
5 1.753573 5.637104
6 -2.539683 -7.282191
7 -1.420543 -4.906298
8 -0.130200 -0.833208
9 0.183062 0.261813
0 1
0 1.000000 0.992504
1 0.992504 1.000000
</pre></div>
</div>
</div>
@@ -797,37 +824,37 @@ 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 0.088104 0.081216 0.088760 0.086997 0.085010 0.080343 0.079306
2 0.0 0.081216 0.075612 0.080764 0.079618 0.078300 0.072530 0.071897
3 0.0 0.088760 0.080764 0.094925 0.092249 0.089310 0.089233 0.087615
4 0.0 0.086997 0.079618 0.092249 0.089982 0.087470 0.086257 0.084927
5 0.0 0.085010 0.078300 0.089310 0.087470 0.085410 0.083021 0.081989
6 0.0 0.080343 0.072530 0.089233 0.086257 0.083021 0.086109 0.084269
7 0.0 0.079306 0.071897 0.087615 0.084927 0.081989 0.084269 0.082642
8 0.0 0.078323 0.071329 0.086021 0.083629 0.080998 0.082431 0.081022
9 0.0 0.077372 0.070810 0.084426 0.082339 0.080026 0.080571 0.079383
10 0.0 0.071946 0.064637 0.081990 0.079001 0.075770 0.080642 0.078768
11 0.0 0.071044 0.064041 0.080699 0.077930 0.074922 0.079218 0.077511
12 0.0 0.070222 0.063524 0.079476 0.076927 0.074144 0.077846 0.076306
13 0.0 0.069475 0.063084 0.078314 0.075987 0.073433 0.076518 0.075145
14 0.0 0.068799 0.062719 0.077203 0.075102 0.072783 0.075222 0.074019
1 0.0 0.092290 0.091376 0.091772 0.091659 0.091579 0.083691 0.083321
2 0.0 0.091376 0.091209 0.090620 0.090923 0.091266 0.082166 0.082105
3 0.0 0.091772 0.090620 0.098069 0.097435 0.096845 0.093556 0.092724
4 0.0 0.091659 0.090923 0.097435 0.097111 0.096833 0.092478 0.091896
5 0.0 0.091579 0.091266 0.096845 0.096833 0.096872 0.091445 0.091113
6 0.0 0.083691 0.082166 0.093556 0.092478 0.091445 0.092007 0.090828
7 0.0 0.083321 0.082105 0.092724 0.091896 0.091113 0.090828 0.089857
8 0.0 0.083051 0.082145 0.091996 0.091418 0.090888 0.089744 0.088982
9 0.0 0.082877 0.082285 0.091369 0.091044 0.090768 0.088754 0.088201
10 0.0 0.075829 0.073985 0.087419 0.086021 0.084663 0.087860 0.086440
11 0.0 0.075277 0.073684 0.086460 0.085272 0.084124 0.086624 0.085384
12 0.0 0.074819 0.073477 0.085603 0.084624 0.083685 0.085484 0.084422
13 0.0 0.074453 0.073363 0.084846 0.084076 0.083348 0.084438 0.083555
14 0.0 0.074180 0.073344 0.084187 0.083627 0.083111 0.083485 0.082779
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.078323 0.077372 0.071946 0.071044 0.070222 0.069475 0.068799
2 0.071329 0.070810 0.064637 0.064041 0.063524 0.063084 0.062719
3 0.086021 0.084426 0.081990 0.080699 0.079476 0.078314 0.077203
4 0.083629 0.082339 0.079001 0.077930 0.076927 0.075987 0.075102
5 0.080998 0.080026 0.075770 0.074922 0.074144 0.073433 0.072783
6 0.082431 0.080571 0.080642 0.079218 0.077846 0.076518 0.075222
7 0.081022 0.079383 0.078768 0.077511 0.076306 0.075145 0.074019
8 0.079622 0.078211 0.076886 0.075797 0.074760 0.073768 0.072813
9 0.078211 0.077033 0.074969 0.074050 0.073183 0.072364 0.071585
10 0.076886 0.074969 0.076632 0.075201 0.073811 0.072452 0.071115
11 0.075797 0.074050 0.075201 0.073904 0.072647 0.071421 0.070216
12 0.074760 0.073183 0.073811 0.072647 0.071523 0.070428 0.069355
13 0.073768 0.072364 0.072452 0.071421 0.070428 0.069465 0.068525
14 0.072813 0.071585 0.071115 0.070216 0.069355 0.068525 0.067719
1 0.083051 0.082877 0.075829 0.075277 0.074819 0.074453 0.074180
2 0.082145 0.082285 0.073985 0.073684 0.073477 0.073363 0.073344
3 0.091996 0.091369 0.087419 0.086460 0.085603 0.084846 0.084187
4 0.091418 0.091044 0.086021 0.085272 0.084624 0.084076 0.083627
5 0.090888 0.090768 0.084663 0.084124 0.083685 0.083348 0.083111
6 0.089744 0.088754 0.087860 0.086624 0.085484 0.084438 0.083485
7 0.088982 0.088201 0.086440 0.085384 0.084422 0.083555 0.082779
8 0.088317 0.087746 0.085108 0.084230 0.083446 0.082756 0.082158
9 0.087746 0.087386 0.083859 0.083159 0.082553 0.082040 0.081620
10 0.085108 0.083859 0.085252 0.083832 0.082501 0.081258 0.080098
11 0.084230 0.083159 0.083832 0.082569 0.081395 0.080305 0.079298
12 0.083446 0.082553 0.082501 0.081395 0.080374 0.079437 0.078582
13 0.082756 0.082040 0.081258 0.080305 0.079437 0.078652 0.077949
14 0.082158 0.081620 0.080098 0.079298 0.078582 0.077949 0.077397
</pre></div>
</div>
</div>
@@ -1016,10 +1043,10 @@ 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 3.967536 1.983164
1 1.983164 2.000755
[[3.9675364 1.98316352]
[1.98316352 2.00075534]]
0 3.956454 1.972286
1 1.972286 1.977089
[[3.95645365 1.97228638]
[1.97228638 1.97708897]]
</pre></div>
</div>
</div>
@@ -1046,8 +1073,8 @@ 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
[[3.9675364 1.98316352]
[1.98316352 2.00075534]]
[[3.95645365 1.97228638]
[1.97228638 1.97708897]]
</pre></div>
</div>
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
@@ -1107,16 +1134,16 @@ 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
5.197738983259782
0.7705527590466072
5.173439546289586
0.7601030735620569
First eigenvector
[0.84977962 0.52713812]
[0.85102768 0.52512084]
Second eigenvector
[-0.52713812 0.84977962]
[-0.52512084 0.85102768]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[-0.84977962 -0.52713812]
[-0.85102768 -0.52512084]
</pre></div>
</div>
</div>