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
2024-10-14 09:13:10 +02:00
parent f1f5b33d5e
commit a7012b5326
140 changed files with 3712 additions and 3488 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/chapter3.html
+51 -37
View File
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
Week 41 Neural networks and constructing a neural network code
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek42.html">
Exercises week 42
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week42.html">
Week 42 Constructing a Neural Network code with examples
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -859,10 +869,10 @@ 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: 0.146141 sec
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.154751 sec
Jackknife Statistics :
original bias std. error
100.139 100.129 0.148776
99.9896 99.9796 0.149524
</pre></div>
</div>
</div>
@@ -1081,7 +1091,7 @@ 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
99.989 15.1792 99.9878 0.152149
100.307 14.9693 100.309 0.149416
</pre></div>
</div>
</div>
@@ -1288,7 +1298,9 @@ Error: 0.08426840630693411
Bias^2: 0.0796891867672603
Var: 0.004579219539673834
0.08426840630693411 &gt;= 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
@@ -1315,7 +1327,9 @@ Error: 0.037813671417389005
Bias^2: 0.033657685071527665
Var: 0.00415598634586135
0.037813671417389005 &gt;= 0.033657685071527665 + 0.00415598634586135 = 0.03781367141738902
Polynomial degree: 7
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 7
Error: 0.02760977349102253
Bias^2: 0.022999498260366312
Var: 0.004610275230656212
@@ -1342,21 +1356,21 @@ Error: 0.07160048164233104
Bias^2: 0.014436800088904942
Var: 0.05716368155342608
0.07160048164233104 &gt;= 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
0.11547777218872497 &gt;= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
Polynomial degree: 13
Error: 0.22842468702219465
Bias^2: 0.01975416527185249
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_6.png" src="_images/chapter3_66_6.png" />
</div>
</div>
<p>The bias-variance tradeoff summarizes the fundamental tension in
@@ -1647,12 +1661,12 @@ Mean squared error on test data: 877.21517262
Degree of polynomial: 23
Mean squared error on training data: 0.00085892
Mean squared error on test data: 5567.04664255
Degree of polynomial: 24
Mean squared error on training data: 0.00084707
Mean squared error on test data: 1325.26124692
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 24
Mean squared error on training data: 0.00084707
Mean squared error on test data: 1325.26124692
Degree of polynomial: 25
Mean squared error on training data: 0.00079125
Mean squared error on test data: 129012.83870189
Degree of polynomial: 26
@@ -1661,19 +1675,19 @@ Mean squared error on test data: 18388.59354079
Degree of polynomial: 27
Mean squared error on training data: 0.00069123
Mean squared error on test data: 2351.97979891
Degree of polynomial: 28
Mean squared error on training data: 0.00062592
Mean squared error on test data: 3983.63037846
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 28
Mean squared error on training data: 0.00062592
Mean squared error on test data: 3983.63037846
Degree of polynomial: 29
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_22458/626635268.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_57183/626635268.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_22458/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
</pre></div>
</div>
@@ -1907,7 +1921,7 @@ 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_22458/3817475779.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_57183/3817475779.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>
@@ -2796,7 +2810,7 @@ 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_22458/4162706317.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_57183/4162706317.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>
@@ -2940,7 +2954,7 @@ 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_22458/3777801602.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_57183/3777801602.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>
@@ -2980,7 +2994,7 @@ 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_22458/438060758.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_57183/438060758.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>
@@ -3015,7 +3029,7 @@ 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_22458/3544313922.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_57183/3544313922.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>
@@ -3068,43 +3082,43 @@ 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 [00:00&lt;00:06, 1.29it/s]
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 [00:01&lt;00:06, 1.18it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 20%|██████████████████████████▊ | 2/10 [00:01&lt;00:06, 1.16it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 30%|█████████████████████████████████████████████████████████▌ | 3/10 [00:02&lt;00:05, 1.29it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 30%|████████████████████████████████████████▏ | 3/10 [00:02&lt;00:05, 1.31it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|████████████████████████████████████████████████████████████████████████████▊ | 4/10 [00:03&lt;00:04, 1.32it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|█████████████████████████████████████████████████████▌ | 4/10 [00:03&lt;00:04, 1.39it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|████████████████████████████████████████████████████████████████████████████████████████████████ | 5/10 [00:03&lt;00:03, 1.54it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|███████████████████████████████████████████████████████████████████ | 5/10 [00:03&lt;00:03, 1.38it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏ | 6/10 [00:04&lt;00:02, 1.65it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|████████████████████████████████████████████████████████████████████████████████▍ | 6/10 [00:04&lt;00:02, 1.44it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▍ | 7/10 [00:04&lt;00:02, 1.44it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|█████████████████████████████████████████████████████████████████████████████████████████████▊ | 7/10 [00:05&lt;00:02, 1.45it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▌ | 8/10 [00:05&lt;00:01, 1.50it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|███████████████████████████████████████████████████████████████████████████████████████████████████████████▏ | 8/10 [00:05&lt;00:01, 1.55it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▊ | 9/10 [00:06&lt;00:00, 1.47it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▌ | 9/10 [00:06&lt;00:00, 1.54it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06&lt;00:00, 1.52it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07&lt;00:00, 1.48it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06&lt;00:00, 1.45it/s]
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07&lt;00:00, 1.43it/s]
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>