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<div class="section" id="robust-regression">
<span id="example-plot-robust-regression-py"></span><h1>Robust regression<a class="headerlink" href="#robust-regression" title="Permalink to this headline">¶</a></h1>
<img alt="../_images/plot_robust_regression_001.png" class="align-center" src="../_images/plot_robust_regression_001.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_robust_regression.py"><tt class="xref download docutils literal"><span class="pre">plot_robust_regression.py</span></tt></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="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">pylab</span> <span class="kn">as</span> <span class="nn">pl</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_regression</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">check_random_state</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">Ridge</span>
<span class="kn">from</span> <span class="nn">lightning.regression</span> <span class="kn">import</span> <span class="n">LinearSVR</span>
<span class="c"># Generate regression data.</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">make_regression</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">n_informative</span><span class="o">=</span><span class="mi">1</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="c"># Add noise.</span>
<span class="n">rs</span> <span class="o">=</span> <span class="n">check_random_state</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">y_train</span> <span class="o">+=</span> <span class="n">rs</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.std.html#numpy.std"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">y_train</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="c"># Add an outlier.</span>
<span class="n">y_train</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span> <span class="o">*=</span> <span class="mi">5</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="mi">100</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">reg</span> <span class="o">=</span> <span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">1e-1</span><span class="p">)</span>
<span class="n">reg</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="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">reg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"Ridge"</span><span class="p">)</span>
<span class="c"># LinearSVR is equivalent to absolute-loss regression (robust regression)</span>
<span class="c"># when epsilon=0.</span>
<span class="n">reg</span> <span class="o">=</span> <span class="n">LinearSVR</span><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">fit_intercept</span><span class="o">=</span><span class="bp">True</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="n">reg</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="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">reg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"Robust"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s">"upper left"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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<p><strong>Total running time of the example:</strong> 0.15 seconds
( 0 minutes 0.15 seconds)</p>
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