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testing local website build

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KarlHenrik
2025-08-11 13:03:14 +02:00
parent 9bf7d8b73a
commit e6d20ce4b2
228 changed files with 8123 additions and 23504 deletions
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doc/LectureNotes/_build/html/chapter4.html
+193 -273
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@@ -28,7 +28,7 @@
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -183,7 +183,7 @@
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">About the course</span></p>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="schedule.html">Teaching schedule with links to material</a></li>
<li class="toctree-l1"><a class="reference internal" href="schedule.html">Course setting</a></li>
<li class="toctree-l1"><a class="reference internal" href="teachers.html">Teachers and Grading</a></li>
<li class="toctree-l1"><a class="reference internal" href="textbooks.html">Textbooks</a></li>
@@ -271,37 +271,6 @@
<div class="dropdown dropdown-launch-buttons">
<button class="btn dropdown-toggle" type="button" data-bs-toggle="dropdown" aria-expanded="false" aria-label="Launch interactive content">
<i class="fas fa-rocket"></i>
</button>
<ul class="dropdown-menu">
<li><a href="https://mybinder.org/v2/git/https%3A//compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/index.html/master?urlpath=tree/chapter4.ipynb" target="_blank"
class="btn btn-sm dropdown-item"
title="Launch on Binder"
data-bs-placement="left" data-bs-toggle="tooltip"
>
<span class="btn__icon-container">
<img alt="Binder logo" src="_static/images/logo_binder.svg">
</span>
<span class="btn__text-container">Binder</span>
</a>
</li>
</ul>
</div>
<div class="dropdown dropdown-download-buttons">
<button class="btn dropdown-toggle" type="button" data-bs-toggle="dropdown" aria-expanded="false" aria-label="Download this page">
<i class="fas fa-download"></i>
@@ -512,111 +481,62 @@ the probability of a given category. This leads us to the logistic function.</p>
<p>The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person’s against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>%matplotlib inline
<span class="c1"># Common imports</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span><span class="p">,</span> <span class="n">Ridge</span><span class="p">,</span> <span class="n">Lasso</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">resample</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span>
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">plt</span><span class="p">,</span> <span class="n">mpl</span>
<span class="n">plt</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s1">&#39;seaborn&#39;</span><span class="p">)</span>
<span class="n">mpl</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;font.family&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;serif&#39;</span>
# Common imports
import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression, Ridge, Lasso
from sklearn.model_selection import train_test_split
from sklearn.utils import resample
from sklearn.metrics import mean_squared_error
from IPython.display import display
from pylab import plt, mpl
plt.style.use(&#39;seaborn&#39;)
mpl.rcParams[&#39;font.family&#39;] = &#39;serif&#39;
<span class="c1"># Where to save the figures and data files</span>
<span class="n">PROJECT_ROOT_DIR</span> <span class="o">=</span> <span class="s2">&quot;Results&quot;</span>
<span class="n">FIGURE_ID</span> <span class="o">=</span> <span class="s2">&quot;Results/FigureFiles&quot;</span>
<span class="n">DATA_ID</span> <span class="o">=</span> <span class="s2">&quot;DataFiles/&quot;</span>
# Where to save the figures and data files
PROJECT_ROOT_DIR = &quot;Results&quot;
FIGURE_ID = &quot;Results/FigureFiles&quot;
DATA_ID = &quot;DataFiles/&quot;
<span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">PROJECT_ROOT_DIR</span><span class="p">):</span>
<span class="n">os</span><span class="o">.</span><span class="n">mkdir</span><span class="p">(</span><span class="n">PROJECT_ROOT_DIR</span><span class="p">)</span>
if not os.path.exists(PROJECT_ROOT_DIR):
os.mkdir(PROJECT_ROOT_DIR)
<span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">FIGURE_ID</span><span class="p">):</span>
<span class="n">os</span><span class="o">.</span><span class="n">makedirs</span><span class="p">(</span><span class="n">FIGURE_ID</span><span class="p">)</span>
if not os.path.exists(FIGURE_ID):
os.makedirs(FIGURE_ID)
<span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">DATA_ID</span><span class="p">):</span>
<span class="n">os</span><span class="o">.</span><span class="n">makedirs</span><span class="p">(</span><span class="n">DATA_ID</span><span class="p">)</span>
if not os.path.exists(DATA_ID):
os.makedirs(DATA_ID)
<span class="k">def</span> <span class="nf">image_path</span><span class="p">(</span><span class="n">fig_id</span><span class="p">):</span>
<span class="k">return</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">FIGURE_ID</span><span class="p">,</span> <span class="n">fig_id</span><span class="p">)</span>
def image_path(fig_id):
return os.path.join(FIGURE_ID, fig_id)
<span class="k">def</span> <span class="nf">data_path</span><span class="p">(</span><span class="n">dat_id</span><span class="p">):</span>
<span class="k">return</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">DATA_ID</span><span class="p">,</span> <span class="n">dat_id</span><span class="p">)</span>
def data_path(dat_id):
return os.path.join(DATA_ID, dat_id)
<span class="k">def</span> <span class="nf">save_fig</span><span class="p">(</span><span class="n">fig_id</span><span class="p">):</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>
def save_fig(fig_id):
plt.savefig(image_path(fig_id) + &quot;.png&quot;, format=&#39;png&#39;)
<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>
infile = open(data_path(&quot;chddata.csv&quot;),&#39;r&#39;)
<span class="c1"># Read the chd data as csv file and organize the data into arrays with age group, age, and chd</span>
<span class="n">chd</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">infile</span><span class="p">,</span> <span class="n">names</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;ID&#39;</span><span class="p">,</span> <span class="s1">&#39;Age&#39;</span><span class="p">,</span> <span class="s1">&#39;Agegroup&#39;</span><span class="p">,</span> <span class="s1">&#39;CHD&#39;</span><span class="p">))</span>
<span class="n">chd</span><span class="o">.</span><span class="n">columns</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;ID&#39;</span><span class="p">,</span> <span class="s1">&#39;Age&#39;</span><span class="p">,</span> <span class="s1">&#39;Agegroup&#39;</span><span class="p">,</span> <span class="s1">&#39;CHD&#39;</span><span class="p">]</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">chd</span><span class="p">[</span><span class="s1">&#39;CHD&#39;</span><span class="p">]</span>
<span class="n">age</span> <span class="o">=</span> <span class="n">chd</span><span class="p">[</span><span class="s1">&#39;Age&#39;</span><span class="p">]</span>
<span class="n">agegroup</span> <span class="o">=</span> <span class="n">chd</span><span class="p">[</span><span class="s1">&#39;Agegroup&#39;</span><span class="p">]</span>
<span class="n">numberID</span> <span class="o">=</span> <span class="n">chd</span><span class="p">[</span><span class="s1">&#39;ID&#39;</span><span class="p">]</span>
<span class="n">display</span><span class="p">(</span><span class="n">chd</span><span class="p">)</span>
# Read the chd data as csv file and organize the data into arrays with age group, age, and chd
chd = pd.read_csv(infile, names=(&#39;ID&#39;, &#39;Age&#39;, &#39;Agegroup&#39;, &#39;CHD&#39;))
chd.columns = [&#39;ID&#39;, &#39;Age&#39;, &#39;Agegroup&#39;, &#39;CHD&#39;]
output = chd[&#39;CHD&#39;]
age = chd[&#39;Age&#39;]
agegroup = chd[&#39;Agegroup&#39;]
numberID = chd[&#39;ID&#39;]
display(chd)
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">age</span><span class="p">,</span> <span class="n">output</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">18</span><span class="p">,</span><span class="mf">70.0</span><span class="p">,</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Age&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;CHD&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Age distribution and Coronary heart disease&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</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="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/matplotlib/style/core.py:137,</span> in <span class="ni">use</span><span class="nt">(style)</span>
<span class="g g-Whitespace"> </span><span class="mi">136</span> <span class="k">try</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">137</span> <span class="n">style</span> <span class="o">=</span> <span class="n">_rc_params_in_file</span><span class="p">(</span><span class="n">style</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">138</span> <span class="k">except</span> <span class="ne">OSError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/matplotlib/__init__.py:866,</span> in <span class="ni">_rc_params_in_file</span><span class="nt">(fname, transform, fail_on_error)</span>
<span class="g g-Whitespace"> </span><span class="mi">865</span> <span class="n">rc_temp</span> <span class="o">=</span> <span class="p">{}</span>
<span class="ne">--&gt; </span><span class="mi">866</span> <span class="k">with</span> <span class="n">_open_file_or_url</span><span class="p">(</span><span class="n">fname</span><span class="p">)</span> <span class="k">as</span> <span class="n">fd</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">867</span> <span class="k">try</span><span class="p">:</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/contextlib.py:119,</span> in <span class="ni">_GeneratorContextManager.__enter__</span><span class="nt">(self)</span>
<span class="g g-Whitespace"> </span><span class="mi">118</span> <span class="k">try</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">119</span> <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gen</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">120</span> <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/matplotlib/__init__.py:843,</span> in <span class="ni">_open_file_or_url</span><span class="nt">(fname)</span>
<span class="g g-Whitespace"> </span><span class="mi">842</span> <span class="n">fname</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">expanduser</span><span class="p">(</span><span class="n">fname</span><span class="p">)</span>
<span class="ne">--&gt; </span><span class="mi">843</span> <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">encoding</span><span class="o">=</span><span class="s1">&#39;utf-8&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">844</span> <span class="k">yield</span> <span class="n">f</span>
<span class="ne">FileNotFoundError</span>: [Errno 2] No such file or directory: &#39;seaborn&#39;
<span class="n">The</span> <span class="n">above</span> <span class="n">exception</span> <span class="n">was</span> <span class="n">the</span> <span class="n">direct</span> <span class="n">cause</span> <span class="n">of</span> <span class="n">the</span> <span class="n">following</span> <span class="n">exception</span><span class="p">:</span>
<span class="ne">OSError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">14</span>
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span>
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">plt</span><span class="p">,</span> <span class="n">mpl</span>
<span class="ne">---&gt; </span><span class="mi">14</span> <span class="n">plt</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s1">&#39;seaborn&#39;</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">mpl</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;font.family&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;serif&#39;</span>
<span class="g g-Whitespace"> </span><span class="mi">17</span> <span class="c1"># Where to save the figures and data files</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/matplotlib/style/core.py:139,</span> in <span class="ni">use</span><span class="nt">(style)</span>
<span class="g g-Whitespace"> </span><span class="mi">137</span> <span class="n">style</span> <span class="o">=</span> <span class="n">_rc_params_in_file</span><span class="p">(</span><span class="n">style</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">138</span> <span class="k">except</span> <span class="ne">OSError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">139</span> <span class="k">raise</span> <span class="ne">OSError</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">140</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">style</span><span class="si">!r}</span><span class="s2"> is not a valid package style, path of style &quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">141</span> <span class="sa">f</span><span class="s2">&quot;file, URL of style file, or library style name (library &quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">142</span> <span class="sa">f</span><span class="s2">&quot;styles are listed in `style.available`)&quot;</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">err</span>
<span class="g g-Whitespace"> </span><span class="mi">143</span> <span class="n">filtered</span> <span class="o">=</span> <span class="p">{}</span>
<span class="nn"> 144 for k</span> in <span class="ni">style: # don&#39;t trigger RcParams.__getitem__</span><span class="nt">(&#39;backend&#39;)</span>
<span class="ne">OSError</span>: &#39;seaborn&#39; is not a valid package style, path of style file, URL of style file, or library style name (library styles are listed in `style.available`)
plt.scatter(age, output, marker=&#39;o&#39;)
plt.axis([18,70.0,-0.1, 1.2])
plt.xlabel(r&#39;Age&#39;)
plt.ylabel(r&#39;CHD&#39;)
plt.title(r&#39;Age distribution and Coronary heart disease&#39;)
plt.show()
</pre></div>
</div>
</div>
@@ -624,14 +544,14 @@ the probability of a given category. This leads us to the logistic function.</p>
<p>What we could attempt however is to plot the mean value for each group.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">agegroupmean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.133</span><span class="p">,</span> <span class="mf">0.250</span><span class="p">,</span> <span class="mf">0.333</span><span class="p">,</span> <span class="mf">0.462</span><span class="p">,</span> <span class="mf">0.625</span><span class="p">,</span> <span class="mf">0.765</span><span class="p">,</span> <span class="mf">0.800</span><span class="p">])</span>
<span class="n">group</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">group</span><span class="p">,</span> <span class="n">agegroupmean</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Age group&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;CHD mean values&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Mean values for each age group&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])
group = np.array([1, 2, 3, 4, 5, 6, 7, 8])
plt.plot(group, agegroupmean, &quot;r-&quot;)
plt.axis([0,9,0, 1.0])
plt.xlabel(r&#39;Age group&#39;)
plt.ylabel(r&#39;CHD mean values&#39;)
plt.title(r&#39;Mean values for each age group&#39;)
plt.show()
</pre></div>
</div>
</div>
@@ -677,60 +597,60 @@ p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
<p>The following code plots the logistic function, the step function and other functions we will encounter from here and on.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="sd">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a</span>
<span class="sd">function that takes any real number, z, and outputs a number (0,1).</span>
<span class="sd">It is useful in neural networks for assigning weights on a relative scale.</span>
<span class="sd">The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a
function that takes any real number, z, and outputs a number (0,1).
It is useful in neural networks for assigning weights on a relative scale.
The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;
<span class="kn">import</span> <span class="nn">numpy</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">math</span> <span class="k">as</span> <span class="nn">mt</span>
import numpy
import matplotlib.pyplot as plt
import math as mt
<span class="n">z</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">.1</span><span class="p">)</span>
<span class="n">sigma_fn</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">z</span><span class="p">:</span> <span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">numpy</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">z</span><span class="p">)))</span>
<span class="n">sigma</span> <span class="o">=</span> <span class="n">sigma_fn</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
z = numpy.arange(-5, 5, .1)
sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))
sigma = sigma_fn(z)
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;z&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;sigmoid function&#39;</span><span class="p">)</span>
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(z, sigma)
ax.set_ylim([-0.1, 1.1])
ax.set_xlim([-5,5])
ax.grid(True)
ax.set_xlabel(&#39;z&#39;)
ax.set_title(&#39;sigmoid function&#39;)
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
plt.show()
<span class="sd">&quot;&quot;&quot;Step Function&quot;&quot;&quot;</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">.02</span><span class="p">)</span>
<span class="n">step_fn</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">z</span><span class="p">:</span> <span class="mf">1.0</span> <span class="k">if</span> <span class="n">z</span> <span class="o">&gt;=</span> <span class="mf">0.0</span> <span class="k">else</span> <span class="mf">0.0</span><span class="p">)</span>
<span class="n">step</span> <span class="o">=</span> <span class="n">step_fn</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
&quot;&quot;&quot;Step Function&quot;&quot;&quot;
z = numpy.arange(-5, 5, .02)
step_fn = numpy.vectorize(lambda z: 1.0 if z &gt;= 0.0 else 0.0)
step = step_fn(z)
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;z&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;step function&#39;</span><span class="p">)</span>
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(z, step)
ax.set_ylim([-0.5, 1.5])
ax.set_xlim([-5,5])
ax.grid(True)
ax.set_xlabel(&#39;z&#39;)
ax.set_title(&#39;step function&#39;)
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
plt.show()
<span class="sd">&quot;&quot;&quot;tanh Function&quot;&quot;&quot;</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">mt</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">mt</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
&quot;&quot;&quot;tanh Function&quot;&quot;&quot;
z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)
t = numpy.tanh(z)
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">mt</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span><span class="mi">2</span><span class="o">*</span><span class="n">mt</span><span class="o">.</span><span class="n">pi</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;z&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;tanh function&#39;</span><span class="p">)</span>
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(z, t)
ax.set_ylim([-1.0, 1.0])
ax.set_xlim([-2*mt.pi,2*mt.pi])
ax.grid(True)
ax.set_xlabel(&#39;z&#39;)
ax.set_title(&#39;tanh function&#39;)
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
plt.show()
</pre></div>
</div>
</div>
@@ -870,31 +790,31 @@ cancer data using Logistic regression as our algorithm for
classification.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.linear_model import LogisticRegression
<span class="c1"># Load the data</span>
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
# Load the data
cancer = load_breast_cancer()
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="c1"># Logistic Regression</span>
<span class="n">logreg</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">&#39;lbfgs&#39;</span><span class="p">)</span>
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy with Logistic Regression: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
<span class="c1">#now scale the data</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># Logistic Regression</span>
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy Logistic Regression with scaled data: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
# Logistic Regression
logreg = LogisticRegression(solver=&#39;lbfgs&#39;)
logreg.fit(X_train, y_train)
print(&quot;Test set accuracy with Logistic Regression: {:.2f}&quot;.format(logreg.score(X_test,y_test)))
#now scale the data
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
# Logistic Regression
logreg.fit(X_train_scaled, y_train)
print(&quot;Test set accuracy Logistic Regression with scaled data: {:.2f}&quot;.format(logreg.score(X_test_scaled,y_test)))
</pre></div>
</div>
</div>
@@ -903,40 +823,40 @@ classification.</p>
We use <strong>Pandas</strong> to compute the correlation matrix.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="c1"># Making a data frame</span>
<span class="n">cancerpd</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">cancer</span><span class="o">.</span><span class="n">feature_names</span><span class="p">)</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.linear_model import LogisticRegression
cancer = load_breast_cancer()
import pandas as pd
# Making a data frame
cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">))</span>
<span class="n">malignant</span> <span class="o">=</span> <span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">benign</span> <span class="o">=</span> <span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
fig, axes = plt.subplots(15,2,figsize=(10,20))
malignant = cancer.data[cancer.target == 0]
benign = cancer.data[cancer.target == 1]
ax = axes.ravel()
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">30</span><span class="p">):</span>
<span class="n">_</span><span class="p">,</span> <span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span> <span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">malignant</span><span class="p">[:,</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span> <span class="o">=</span> <span class="n">bins</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">benign</span><span class="p">[:,</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span> <span class="o">=</span> <span class="n">bins</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">feature_names</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Feature magnitude&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Frequency&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">&quot;Malignant&quot;</span><span class="p">,</span> <span class="s2">&quot;Benign&quot;</span><span class="p">],</span> <span class="n">loc</span> <span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
for i in range(30):
_, bins = np.histogram(cancer.data[:,i], bins =50)
ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)
ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)
ax[i].set_title(cancer.feature_names[i])
ax[i].set_yticks(())
ax[0].set_xlabel(&quot;Feature magnitude&quot;)
ax[0].set_ylabel(&quot;Frequency&quot;)
ax[0].legend([&quot;Malignant&quot;, &quot;Benign&quot;], loc =&quot;best&quot;)
fig.tight_layout()
plt.show()
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
<span class="n">correlation_matrix</span> <span class="o">=</span> <span class="n">cancerpd</span><span class="o">.</span><span class="n">corr</span><span class="p">()</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># use the heatmap function from seaborn to plot the correlation matrix</span>
<span class="c1"># annot = True to print the values inside the square</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">correlation_matrix</span><span class="p">,</span> <span class="n">annot</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
import seaborn as sns
correlation_matrix = cancerpd.corr().round(1)
# use the heatmap function from seaborn to plot the correlation matrix
# annot = True to print the values inside the square
plt.figure(figsize=(15,8))
sns.heatmap(data=correlation_matrix, annot=True)
plt.show()
</pre></div>
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@@ -954,7 +874,7 @@ matrix.</p>
<p>We constructed this matrix using <strong>pandas</strong> via the statements</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">cancerpd</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">cancer</span><span class="o">.</span><span class="n">feature_names</span><span class="p">)</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)
</pre></div>
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@@ -962,7 +882,7 @@ matrix.</p>
<p>and then</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">correlation_matrix</span> <span class="o">=</span> <span class="n">cancerpd</span><span class="o">.</span><span class="n">corr</span><span class="p">()</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>correlation_matrix = cancerpd.corr().round(1)
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@@ -987,50 +907,50 @@ Based on this we can then define the accuracy score as the sum of correctly pred
\]</div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.linear_model import LogisticRegression
<span class="c1"># Load the data</span>
<span class="n">cancer</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
# Load the data
cancer = load_breast_cancer()
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">cancer</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="c1"># Logistic Regression</span>
<span class="n">logreg</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">&#39;lbfgs&#39;</span><span class="p">)</span>
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy with Logistic Regression: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
<span class="c1">#now scale the data</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
<span class="n">scaler</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>
<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_train_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_test_scaled</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># Logistic Regression</span>
<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy Logistic Regression with scaled data: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
# Logistic Regression
logreg = LogisticRegression(solver=&#39;lbfgs&#39;)
logreg.fit(X_train, y_train)
print(&quot;Test set accuracy with Logistic Regression: {:.2f}&quot;.format(logreg.score(X_test,y_test)))
#now scale the data
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
# Logistic Regression
logreg.fit(X_train_scaled, y_train)
print(&quot;Test set accuracy Logistic Regression with scaled data: {:.2f}&quot;.format(logreg.score(X_test_scaled,y_test)))
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">LabelEncoder</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
<span class="c1">#Cross validation</span>
<span class="n">accuracy</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">logreg</span><span class="p">,</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">,</span><span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)[</span><span class="s1">&#39;test_score&#39;</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="n">accuracy</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy with Logistic Regression and scaled data: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
from sklearn.preprocessing import LabelEncoder
from sklearn.model_selection import cross_validate
#Cross validation
accuracy = cross_validate(logreg,X_test_scaled,y_test,cv=10)[&#39;test_score&#39;]
print(accuracy)
print(&quot;Test set accuracy with Logistic Regression and scaled data: {:.2f}&quot;.format(logreg.score(X_test_scaled,y_test)))
<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</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="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="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">y_probas</span> <span class="o">=</span> <span class="n">logreg</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
import scikitplot as skplt
y_pred = logreg.predict(X_test_scaled)
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
plt.show()
y_probas = logreg.predict_proba(X_test_scaled)
skplt.metrics.plot_roc(y_test, y_probas)
plt.show()
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
plt.show()
</pre></div>
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