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<li><a class="reference internal" href="#">Isotonic Regression</a></li>
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<div class="section" id="isotonic-regression">
<span id="example-plot-isotonic-regression-py"></span><h1>Isotonic Regression<a class="headerlink" href="#isotonic-regression" title="Permalink to this headline">¶</a></h1>
<p>An illustration of the isotonic regression on generated data. The
isotonic regression finds a non-decreasing approximation of a function
while minimizing the mean squared error on the training data. The benefit
of such a model is that it does not assume any form for the target
function such as linearity. For comparison a linear regression is also
presented.</p>
<img alt="../_images/plot_isotonic_regression_001.png" class="align-center" src="../_images/plot_isotonic_regression_001.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_isotonic_regression.py"><code class="xref download docutils literal"><span class="pre">plot_isotonic_regression.py</span></code></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">__doc__</span><span class="p">)</span>
<span class="c1"># Author: Nelle Varoquaux <[email protected]></span>
<span class="c1"># Alexandre Gramfort <[email protected]></span>
<span class="c1"># Licence: BSD</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.collections</span> <span class="kn">import</span> <a href="http://matplotlib.org/api/collections_api.html#matplotlib.collections.LineCollection"><span class="n">LineCollection</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression"><span class="n">LinearRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.isotonic</span> <span class="kn">import</span> <a href="../modules/generated/sklearn.isotonic.IsotonicRegression.html#sklearn.isotonic.IsotonicRegression"><span class="n">IsotonicRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <a href="../modules/generated/sklearn.utils.check_random_state.html#sklearn.utils.check_random_state"><span class="n">check_random_state</span></a>
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">x</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.arange.html#numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="n">rs</span> <span class="o">=</span> <a href="../modules/generated/sklearn.utils.check_random_state.html#sklearn.utils.check_random_state"><span class="n">check_random_state</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">rs</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="o">-</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">n</span><span class="p">,))</span> <span class="o">+</span> <span class="mf">50.</span> <span class="o">*</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.log.html#numpy.log"><span class="n">np</span><span class="o">.</span><span class="n">log</span></a><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.arange.html#numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">n</span><span class="p">))</span>
<span class="c1">###############################################################################</span>
<span class="c1"># Fit IsotonicRegression and LinearRegression models</span>
<span class="n">ir</span> <span class="o">=</span> <a href="../modules/generated/sklearn.isotonic.IsotonicRegression.html#sklearn.isotonic.IsotonicRegression"><span class="n">IsotonicRegression</span></a><span class="p">()</span>
<span class="n">y_</span> <span class="o">=</span> <span class="n">ir</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">lr</span> <span class="o">=</span> <a href="../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression"><span class="n">LinearRegression</span></a><span class="p">()</span>
<span class="n">lr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">y</span><span class="p">)</span> <span class="c1"># x needs to be 2d for LinearRegression</span>
<span class="c1">###############################################################################</span>
<span class="c1"># plot result</span>
<span class="n">segments</span> <span class="o">=</span> <span class="p">[[[</span><span class="n">i</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span> <span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">y_</span><span class="p">[</span><span class="n">i</span><span class="p">]]]</span> <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="n">n</span><span class="p">)]</span>
<span class="n">lc</span> <span class="o">=</span> <a href="http://matplotlib.org/api/collections_api.html#matplotlib.collections.LineCollection"><span class="n">LineCollection</span></a><span class="p">(</span><span class="n">segments</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">lc</span><span class="o">.</span><span class="n">set_array</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.ones.html#numpy.ones"><span class="n">np</span><span class="o">.</span><span class="n">ones</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)))</span>
<span class="n">lc</span><span class="o">.</span><span class="n">set_linewidths</span><span class="p">(</span><span class="mf">0.5</span> <span class="o">*</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.ones.html#numpy.ones"><span class="n">np</span><span class="o">.</span><span class="n">ones</span></a><span class="p">(</span><span class="n">n</span><span class="p">))</span>
<span class="n">fig</span> <span class="o">=</span> <a href="http://matplotlib.org/api/figure_api.html#matplotlib.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">'r.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y_</span><span class="p">,</span> <span class="s1">'g.-'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">lr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">x</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]),</span> <span class="s1">'b-'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.gca"><span class="n">plt</span><span class="o">.</span><span class="n">gca</span></a><span class="p">()</span><span class="o">.</span><span class="n">add_collection</span><span class="p">(</span><span class="n">lc</span><span class="p">)</span>
<a href="http://matplotlib.org/api/legend_api.html#matplotlib.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">((</span><span class="s1">'Data'</span><span class="p">,</span> <span class="s1">'Isotonic Fit'</span><span class="p">,</span> <span class="s1">'Linear Fit'</span><span class="p">),</span> <span class="n">loc</span><span class="o">=</span><span class="s1">'lower right'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Isotonic regression'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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<p><strong>Total running time of the example:</strong> 0.08 seconds
( 0 minutes 0.08 seconds)</p>
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