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
2024-09-10 12:06:15 +02:00
parent 4a3985783f
commit 4e5c11dfa3
143 changed files with 2073 additions and 6207 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/chapter3.html
+56 -31
View File
@@ -275,7 +275,34 @@ const thebe_selector_output = ".output, .cell_output"
</li>
<li class="toctree-l1">
<a class="reference internal" href="week36.html">
Week 36: Linear Rgeression and Statistical interpretations
Week 36: Linear Regression and Statistical interpretations
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek37.html">
Exercises week 37
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week37.html">
Week 37: Statistical interpretations and Resampling Methods
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek38.html">
Exercises week 38
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Projects
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="project1.html">
Project 1 on Machine Learning, deadline October 7 (midnight), 2024
</a>
</li>
</ul>
@@ -797,10 +824,10 @@ 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: 0.148282 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.14708 sec
Jackknife Statistics :
original bias std. error
99.9492 99.9392 0.150707
100.034 100.024 0.147836
</pre></div>
</div>
</div>
@@ -1019,7 +1046,7 @@ 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
100.154 14.9603 100.154 0.149425
100.179 15.0422 100.179 0.151522
</pre></div>
</div>
</div>
@@ -1236,9 +1263,7 @@ Error: 0.06547790180152355
Bias^2: 0.06208238634231949
Var: 0.0033955154592040936
0.06547790180152355 &gt;= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 4
Polynomial degree: 4
Error: 0.06844519414009445
Bias^2: 0.06453579006728324
Var: 0.003909404072811226
@@ -1265,14 +1290,14 @@ Error: 0.017355848195593347
Bias^2: 0.010331721306655127
Var: 0.007024126888938232
0.017355848195593347 &gt;= 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 &gt;= 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
@@ -1294,7 +1319,7 @@ Var: 0.20867052175034223
0.22842468702219465 &gt;= 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_3.png" src="_images/chapter3_66_3.png" />
</div>
</div>
<p>The bias-variance tradeoff summarizes the fundamental tension in
@@ -1609,9 +1634,9 @@ 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_49101/626635268.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_1390/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(trainingerror), label=&#39;Training Error&#39;)
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_49101/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_1390/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
</pre></div>
</div>
@@ -1845,7 +1870,7 @@ 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_49101/3817475779.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_1390/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label=&#39;Test Error&#39;)
</pre></div>
</div>
@@ -2734,7 +2759,7 @@ 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_49101/4162706317.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_1390/4162706317.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>
@@ -2878,7 +2903,7 @@ 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_49101/3777801602.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_1390/3777801602.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>
@@ -2918,7 +2943,7 @@ 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_49101/438060758.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_1390/438060758.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>
@@ -2953,7 +2978,7 @@ 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_49101/3544313922.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_1390/3544313922.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>
@@ -3006,43 +3031,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
</div>
</div>
<div class="cell_output docutils container">
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0%| | 0/10 [00:00&lt;?, ?it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0%| | 0/10 [00:00&lt;?, ?it/s]
</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/linear_model/_coordinate_descent.py:628: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
model = cd_fast.enet_coordinate_descent(
10%|██████████ | 1/10 [00:01&lt;00:11, 1.25s/it]
10%|███████████████████▏ | 1/10 [00:00&lt;00:07, 1.14it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 20%|████████████████████ | 2/10 [00:02&lt;00:09, 1.24s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 20%|██████████████████████████████████████▍ | 2/10 [00:01&lt;00:07, 1.13it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 30%|██████████████████████████████ | 3/10 [00:03&lt;00:07, 1.14s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 30%|█████████████████████████████████████████████████████████▌ | 3/10 [00:02&lt;00:05, 1.24it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|████████████████████████████████████████ | 4/10 [00:04&lt;00:06, 1.01s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|████████████████████████████████████████████████████████████████████████████▊ | 4/10 [00:03&lt;00:04, 1.31it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|██████████████████████████████████████████████████ | 5/10 [00:05&lt;00:04, 1.01it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|████████████████████████████████████████████████████████████████████████████████████████████████ | 5/10 [00:03&lt;00:03, 1.33it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|████████████████████████████████████████████████████████████ | 6/10 [00:06&lt;00:03, 1.00it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ | 6/10 [00:04&lt;00:03, 1.30it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████ | 7/10 [00:07&lt;00:03, 1.02s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▍ | 7/10 [00:05&lt;00:02, 1.28it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|████████████████████████████████████████████████████████████████████████████████ | 8/10 [00:08&lt;00:01, 1.02it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▌ | 8/10 [00:06&lt;00:01, 1.33it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|██████████████████████████████████████████████████████████████████████████████████████████ | 9/10 [00:09&lt;00:01, 1.01s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▊ | 9/10 [00:07&lt;00:00, 1.30it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:10&lt;00:00, 1.00s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07&lt;00:00, 1.35it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:10&lt;00:00, 1.03s/it]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07&lt;00:00, 1.30it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>