updating figures

2021-09-13 11:54:18 +02:00
parent c30998b68a
commit 1af325e7fb
55 changed files with 4282 additions and 2361 deletions
@@ -55,7 +55,7 @@
    <link rel="index" title="Index" href="genindex.html" />
    <link rel="search" title="Search" href="search.html" />
    <link rel="next" title="7. Support Vector Machines, overarching aims" href="chapter5.html" />
-    <link rel="prev" title="5. Ridge and Lasso Regression" href="chapter3.html" />
+    <link rel="prev" title="5. Resampling Methods" href="chapter3.html" />
    <meta name="viewport" content="width=device-width, initial-scale=1" />
    <meta name="docsearch:language" content="en" />
    
@@ -144,12 +144,12 @@
 </li>
 <li class="toctree-l1">
  <a class="reference internal" href="chapter2.html">
-   4. Resampling Methods
+   4. Ridge and Lasso Regression
  </a>
 </li>
 <li class="toctree-l1">
  <a class="reference internal" href="chapter3.html">
-   5. Ridge and Lasso Regression
+   5. Resampling Methods
  </a>
 </li>
 <li class="toctree-l1 current active">
@@ -725,18 +725,112 @@ the probability of a given category. This leads us to the logistic function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">FileNotFoundError</span><span class="g g-Whitespace">                         </span>Traceback (most recent call last)
-<span class="o">&lt;</span><span class="n">ipython</span><span class="o">-</span><span class="nb">input</span><span class="o">-</span><span class="mi">1</span><span class="o">-</span><span class="n">a77d5ac269b2</span><span class="o">&gt;</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span>     <span class="n">plt</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">image_path</span><span class="p">(</span><span class="n">fig_id</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;.png&quot;</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;png&#39;</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> 
-<span class="ne">---&gt; </span><span class="mi">40</span> <span class="n">infile</span> <span class="o">=</span> <span class="nb">open</span><span class="p">(</span><span class="n">data_path</span><span class="p">(</span><span class="s2">&quot;chddata.csv&quot;</span><span class="p">),</span><span class="s1">&#39;r&#39;</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">41</span> 
-<span class="g g-Whitespace">     </span><span class="mi">42</span> <span class="c1"># Read the chd data as  csv file and organize the data into arrays with age group, age, and chd</span>
+<div class="output text_html"><div>
+<style scoped>
+    .dataframe tbody tr th:only-of-type {
+        vertical-align: middle;
+    }

-<span class="ne">FileNotFoundError</span>: [Errno 2] No such file or directory: &#39;DataFiles/chddata.csv&#39;
-</pre></div>
-</div>
+    .dataframe tbody tr th {
+        vertical-align: top;
+    }
+
+    .dataframe thead th {
+        text-align: right;
+    }
+</style>
+<table border="1" class="dataframe">
+  <thead>
+    <tr style="text-align: right;">
+      <th></th>
+      <th>ID</th>
+      <th>Age</th>
+      <th>Agegroup</th>
+      <th>CHD</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <th>0</th>
+      <td>1</td>
+      <td>21</td>
+      <td>1</td>
+      <td>0</td>
+    </tr>
+    <tr>
+      <th>1</th>
+      <td>2</td>
+      <td>23</td>
+      <td>1</td>
+      <td>0</td>
+    </tr>
+    <tr>
+      <th>2</th>
+      <td>3</td>
+      <td>25</td>
+      <td>1</td>
+      <td>1</td>
+    </tr>
+    <tr>
+      <th>3</th>
+      <td>4</td>
+      <td>29</td>
+      <td>1</td>
+      <td>0</td>
+    </tr>
+    <tr>
+      <th>4</th>
+      <td>5</td>
+      <td>21</td>
+      <td>1</td>
+      <td>0</td>
+    </tr>
+    <tr>
+      <th>...</th>
+      <td>...</td>
+      <td>...</td>
+      <td>...</td>
+      <td>...</td>
+    </tr>
+    <tr>
+      <th>95</th>
+      <td>96</td>
+      <td>61</td>
+      <td>8</td>
+      <td>1</td>
+    </tr>
+    <tr>
+      <th>96</th>
+      <td>97</td>
+      <td>69</td>
+      <td>8</td>
+      <td>1</td>
+    </tr>
+    <tr>
+      <th>97</th>
+      <td>98</td>
+      <td>65</td>
+      <td>8</td>
+      <td>1</td>
+    </tr>
+    <tr>
+      <th>98</th>
+      <td>99</td>
+      <td>64</td>
+      <td>8</td>
+      <td>1</td>
+    </tr>
+    <tr>
+      <th>99</th>
+      <td>100</td>
+      <td>63</td>
+      <td>8</td>
+      <td>0</td>
+    </tr>
+  </tbody>
+</table>
+<p>100 rows × 4 columns</p>
+</div></div><img alt="_images/chapter4_5_1.png" src="_images/chapter4_5_1.png" />
 </div>
 </div>
 <p>What we could attempt however is to plot the mean value for each group.</p>
@@ -753,6 +847,9 @@ the probability of a given category. This leads us to the logistic function.</p>
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<img alt="_images/chapter4_7_0.png" src="_images/chapter4_7_0.png" />
+</div>
 </div>
 <p>We are now trying to find a function <span class="math notranslate nohighlight">\(f(y\vert x)\)</span>, that is a function which gives us an expected value for the output <span class="math notranslate nohighlight">\(y\)</span> with a given input <span class="math notranslate nohighlight">\(x\)</span>.
 In standard linear regression with a linear dependence on <span class="math notranslate nohighlight">\(x\)</span>, we would write this in terms of our model</p>
@@ -852,6 +949,11 @@ p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<img alt="_images/chapter4_13_0.png" src="_images/chapter4_13_0.png" />
+<img alt="_images/chapter4_13_1.png" src="_images/chapter4_13_1.png" />
+<img alt="_images/chapter4_13_2.png" src="_images/chapter4_13_2.png" />
+</div>
 </div>
 <p>We assume now that we have two classes with <span class="math notranslate nohighlight">\(y_i\)</span> either <span class="math notranslate nohighlight">\(0\)</span> or <span class="math notranslate nohighlight">\(1\)</span>. Furthermore we assume also that we have only two parameters <span class="math notranslate nohighlight">\(\beta\)</span> in our fitting of the Sigmoid function, that is we define probabilities</p>
 <div class="math notranslate nohighlight">
@@ -1016,6 +1118,24 @@ classification.</p>
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
+(143, 30)
+Test set accuracy with Logistic Regression: 0.94
+Test set accuracy Logistic Regression with scaled data: 0.96
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):
+STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
+
+Increase the number of iterations (max_iter) or scale the data as shown in:
+    https://scikit-learn.org/stable/modules/preprocessing.html
+Please also refer to the documentation for alternative solver options:
+    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
+  n_iter_i = _check_optimize_result(
+</pre></div>
+</div>
+</div>
 </div>
 <p>In addition to the above scores, we could also study the covariance (and the correlation matrix).
 We use <strong>Pandas</strong> to compute the correlation matrix.</p>
@@ -1058,6 +1178,10 @@ We use <strong>Pandas</strong> to compute the correlation matrix.</p>
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<img alt="_images/chapter4_51_0.png" src="_images/chapter4_51_0.png" />
+<img alt="_images/chapter4_51_1.png" src="_images/chapter4_51_1.png" />
+</div>
 </div>
 <p>In the above example we note two things. In the first plot we display
 the overlap of benign and malignant tumors as functions of the various
@@ -1138,6 +1262,39 @@ applications. This will be discussed later this semester (<a class="reference ex
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
+(143, 30)
+Test set accuracy with Logistic Regression: 0.94
+Test set accuracy Logistic Regression with scaled data: 0.96
+[1.         1.         1.         1.         1.         1.
+ 1.         1.         0.92857143 0.92857143]
+Test set accuracy with Logistic Regression  and scaled data: 0.96
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):
+STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
+
+Increase the number of iterations (max_iter) or scale the data as shown in:
+    https://scikit-learn.org/stable/modules/preprocessing.html
+Please also refer to the documentation for alternative solver options:
+    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
+  n_iter_i = _check_optimize_result(
+</pre></div>
+</div>
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="o">&lt;</span><span class="n">ipython</span><span class="o">-</span><span class="nb">input</span><span class="o">-</span><span class="mi">8</span><span class="o">-</span><span class="mi">12</span><span class="n">adb44b1c20</span><span class="o">&gt;</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
+<span class="g g-Whitespace">     </span><span class="mi">34</span> 
+<span class="g g-Whitespace">     </span><span class="mi">35</span> 
+<span class="ne">---&gt; </span><span class="mi">36</span> <span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
+<span class="g g-Whitespace">     </span><span class="mi">37</span> <span class="n">y_pred</span> <span class="o">=</span> <span class="n">logreg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;scikitplot&#39;
+</pre></div>
+</div>
+</div>
 </div>
 </div>
 <div class="section" id="optimization-the-central-part-of-any-machine-learning-algortithm">
@@ -2256,7 +2413,7 @@ function.</p>
        
        <div class='prev-next-bottom'>
            
-    <a class='left-prev' id="prev-link" href="chapter3.html" title="previous page"><span class="section-number">5. </span>Ridge and Lasso Regression</a>
+    <a class='left-prev' id="prev-link" href="chapter3.html" title="previous page"><span class="section-number">5. </span>Resampling Methods</a>
    <a class='right-next' id="next-link" href="chapter5.html" title="next page"><span class="section-number">7. </span>Support Vector Machines, overarching aims</a>

        </div>