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

updated book

Browse Source
This commit is contained in:
Morten Hjorth-Jensen
2024-09-11 05:36:59 +02:00
parent 19a064b629
commit 3b762e5606
42 changed files with 580 additions and 524 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/week37.html
+38 -30
View File
@@ -1624,7 +1624,7 @@ 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
100.211 14.8834 100.212 0.149388
100.213 14.98 100.211 0.149466
</pre></div>
</div>
</div>
@@ -1844,7 +1844,9 @@ 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
@@ -1866,14 +1868,14 @@ Error: 0.05227921801205686
Bias^2: 0.0481872773043029
Var: 0.004091940707753939
0.05227921801205686 &gt;= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 6
Polynomial degree: 6
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
@@ -1895,7 +1897,9 @@ Error: 0.021592704588025025
Bias^2: 0.010516485576645508
Var: 0.011076219011379514
0.021592704588025025 &gt;= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
Polynomial degree: 11
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 11
Error: 0.07160048164233104
Bias^2: 0.014436800088904942
Var: 0.05716368155342608
@@ -1912,7 +1916,7 @@ Var: 0.20867052175034223
0.22842468702219465 &gt;= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
</pre></div>
</div>
<img alt="_images/week37_139_4.png" src="_images/week37_139_4.png" />
<img alt="_images/week37_139_6.png" src="_images/week37_139_6.png" />
</div>
</div>
</div>
@@ -2263,29 +2267,31 @@ Mean squared error on test data: 10.50427787
Degree of polynomial: 7
Mean squared error on training data: 0.47313680
Mean squared error on test data: 1.53738247
Degree of polynomial: 8
Mean squared error on training data: 0.04926746
Mean squared error on test data: 0.14629156
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 9
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 8
Mean squared error on training data: 0.04926746
Mean squared error on test data: 0.14629156
Degree of polynomial: 9
Mean squared error on training data: 0.02546675
Mean squared error on test data: 0.11202337
Degree of polynomial: 10
Mean squared error on training data: 0.02424794
Mean squared error on test data: 0.22467274
Degree of polynomial: 11
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 11
Mean squared error on training data: 0.01594452
Mean squared error on test data: 1.07641937
Degree of polynomial: 12
Mean squared error on training data: 0.00805074
Mean squared error on test data: 0.04295757
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 13
Degree of polynomial: 13
Mean squared error on training data: 0.00781918
Mean squared error on test data: 0.56965674
Degree of polynomial: 14
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 14
Mean squared error on training data: 0.00465099
Mean squared error on test data: 0.28443039
Degree of polynomial: 15
@@ -2305,29 +2311,31 @@ Mean squared error on test data: 429.25695398
Degree of polynomial: 19
Mean squared error on training data: 0.00154853
Mean squared error on test data: 239.97065359
Degree of polynomial: 20
Mean squared error on training data: 0.00140846
Mean squared error on test data: 1350.24493666
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 21
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 20
Mean squared error on training data: 0.00140846
Mean squared error on test data: 1350.24493666
Degree of polynomial: 21
Mean squared error on training data: 0.00119688
Mean squared error on test data: 1840.50530832
Degree of polynomial: 22
Mean squared error on training data: 0.00092898
Mean squared error on test data: 1184.60929685
Degree of polynomial: 23
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 23
Mean squared error on training data: 0.00089193
Mean squared error on test data: 3892.17483760
Degree of polynomial: 24
Mean squared error on training data: 0.00083355
Mean squared error on test data: 1332.46736215
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
Degree of polynomial: 25
Mean squared error on training data: 0.00079904
Mean squared error on test data: 7577.76690383
Degree of polynomial: 26
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 26
Mean squared error on training data: 0.00075590
Mean squared error on test data: 1079.36895644
Degree of polynomial: 27
@@ -2343,13 +2351,13 @@ Mean squared error on training data: 0.00063866
Mean squared error on test data: 3099.60342978
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_1579/626635268.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_6729/626635268.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_1579/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_6729/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
</pre></div>
</div>
<img alt="_images/week37_148_9.png" src="_images/week37_148_9.png" />
<img alt="_images/week37_148_11.png" src="_images/week37_148_11.png" />
</div>
</div>
<p>Note that we kept the intercept column in the fitting here. This means that we need to set the <strong>intercept</strong> in the call to the <strong>Scikit-Learn</strong> function as <strong>False</strong>. Alternatively, we could have set up the design matrix <span class="math notranslate nohighlight">\(X\)</span> without the first column of ones.</p>
@@ -2430,7 +2438,7 @@ Mean squared error on test data: 3099.60342978
</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_1579/3817475779.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_6729/3817475779.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>