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<li><a class="reference internal" href="#">Plot Ridge coefficients as a function of the regularization</a></li>
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<div class="section" id="plot-ridge-coefficients-as-a-function-of-the-regularization">
<span id="example-linear-model-plot-ridge-path-py"></span><h1>Plot Ridge coefficients as a function of the regularization<a class="headerlink" href="#plot-ridge-coefficients-as-a-function-of-the-regularization" title="Permalink to this headline">¶</a></h1>
<p>Shows the effect of collinearity in the coefficients of an estimator.</p>
<p><a class="reference internal" href="../../modules/generated/sklearn.linear_model.Ridge.html#sklearn.linear_model.Ridge" title="sklearn.linear_model.Ridge"><code class="xref py py-class docutils literal"><span class="pre">Ridge</span></code></a> Regression is the estimator used in this example.
Each color represents a different feature of the
coefficient vector, and this is displayed as a function of the
regularization parameter.</p>
<p>At the end of the path, as alpha tends toward zero
and the solution tends towards the ordinary least squares, coefficients
exhibit big oscillations.</p>
<img alt="../../_images/plot_ridge_path_001.png" class="align-center" src="../../_images/plot_ridge_path_001.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_ridge_path.py"><code class="xref download docutils literal"><span class="pre">plot_ridge_path.py</span></code></a></p>
<div class="highlight-python"><div class="highlight"><pre>
<span class="c1"># Author: Fabian Pedregosa -- <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<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">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
<span class="c1"># X is the 10x10 Hilbert matrix</span>
<span class="n">X</span> <span class="o">=</span> <span class="mf">1.</span> <span class="o">/</span> <span class="p">(</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="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</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="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)[:,</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/arrays.indexing.html#numpy.newaxis"><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span></a><span class="p">])</span>
<span class="n">y</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="mi">10</span><span class="p">)</span>
<span class="c1">###############################################################################</span>
<span class="c1"># Compute paths</span>
<span class="n">n_alphas</span> <span class="o">=</span> <span class="mi">200</span>
<span class="n">alphas</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.logspace.html#numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="n">n_alphas</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">Ridge</span><span class="p">(</span><span class="n">fit_intercept</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="n">coefs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">alphas</span><span class="p">:</span>
<span class="n">clf</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">a</span><span class="p">)</span>
<span class="n">clf</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">y</span><span class="p">)</span>
<span class="n">coefs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">)</span>
<span class="c1">###############################################################################</span>
<span class="c1"># Display results</span>
<span class="n">ax</span> <span class="o">=</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="n">ax</span><span class="o">.</span><span class="n">set_color_cycle</span><span class="p">([</span><span class="s1">'b'</span><span class="p">,</span> <span class="s1">'r'</span><span class="p">,</span> <span class="s1">'g'</span><span class="p">,</span> <span class="s1">'c'</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">,</span> <span class="s1">'y'</span><span class="p">,</span> <span class="s1">'m'</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">alphas</span><span class="p">,</span> <span class="n">coefs</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xscale</span><span class="p">(</span><span class="s1">'log'</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="n">ax</span><span class="o">.</span><span class="n">get_xlim</span><span class="p">()[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="c1"># reverse axis</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'alpha'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'weights'</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">'Ridge coefficients as a function of the regularization'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/axis_api.html#matplotlib.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</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>
</div>
<p><strong>Total running time of the example:</strong> 0.20 seconds
( 0 minutes 0.20 seconds)</p>
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