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class="body"> <div class="section" id="lasso-and-elastic-net"> <span id="example-linear-model-plot-lasso-coordinate-descent-path-py"></span><h1>Lasso and Elastic Net<a class="headerlink" href="#lasso-and-elastic-net" title="Permalink to this headline">ΒΆ</a></h1> <p>Lasso and elastic net (L1 and L2 penalisation) implemented using a coordinate descent.</p> <img alt="auto_examples/linear_model/images/plot_lasso_coordinate_descent_path.png" class="align-center" src="auto_examples/linear_model/images/plot_lasso_coordinate_descent_path.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_lasso_coordinate_descent_path.py"><tt class="xref download docutils literal"><span class="pre">plot_lasso_coordinate_descent_path.py</span></tt></a></p> <div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">__doc__</span> <span class="c"># Author: Alexandre Gramfort <alexandre.gramfort@inria.fr></span> <span class="c"># License: BSD Style.</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">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">lasso_path</span><span class="p">,</span> <span class="n">enet_path</span> <span class="kn">from</span> <span class="nn">scikits.learn</span> <span class="kn">import</span> <span class="n">datasets</span> <span class="n">diabetes</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_diabetes</span><span class="p">()</span> <span class="n">X</span> <span class="o">=</span> <span class="n">diabetes</span><span class="o">.</span><span class="n">data</span> <span class="n">y</span> <span class="o">=</span> <span class="n">diabetes</span><span class="o">.</span><span class="n">target</span> <span class="n">X</span> <span class="o">/=</span> <span class="n">X</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c"># Standardize data (easier to set the rho parameter)</span> <span class="c">################################################################################</span> <span class="c"># Compute paths</span> <span class="n">eps</span> <span class="o">=</span> <span class="mf">5e-3</span> <span class="c"># the smaller it is the longer is the path</span> <span class="k">print</span> <span class="s">"Computing regularization path using the lasso..."</span> <span class="n">models</span> <span class="o">=</span> <span class="n">lasso_path</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">eps</span><span class="o">=</span><span class="n">eps</span><span class="p">)</span> <span class="n">alphas_lasso</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="n">model</span><span class="o">.</span><span class="n">alpha</span> <span class="k">for</span> <span class="n">model</span> <span class="ow">in</span> <span class="n">models</span><span class="p">])</span> <span class="n">coefs_lasso</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="n">model</span><span class="o">.</span><span class="n">coef_</span> <span class="k">for</span> <span class="n">model</span> <span class="ow">in</span> <span class="n">models</span><span class="p">])</span> <span class="k">print</span> <span class="s">"Computing regularization path using the elastic net..."</span> <span class="n">models</span> <span class="o">=</span> <span class="n">enet_path</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">eps</span><span class="o">=</span><span class="n">eps</span><span class="p">,</span> <span class="n">rho</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span> <span class="n">alphas_enet</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="n">model</span><span class="o">.</span><span class="n">alpha</span> <span class="k">for</span> <span class="n">model</span> <span class="ow">in</span> <span class="n">models</span><span class="p">])</span> <span class="n">coefs_enet</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="n">model</span><span class="o">.</span><span class="n">coef_</span> <span class="k">for</span> <span class="n">model</span> <span class="ow">in</span> <span class="n">models</span><span class="p">])</span> <span class="c">################################################################################</span> <span class="c"># Display results</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">gca</span><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="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="s">'b'</span><span class="p">,</span> <span class="s">'r'</span><span class="p">,</span> <span class="s">'g'</span><span class="p">,</span> <span class="s">'c'</span><span class="p">,</span> <span class="s">'k'</span><span class="p">])</span> <span class="n">l1</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">coefs_lasso</span><span class="p">)</span> <span class="n">l2</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">coefs_enet</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">'--'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'-Log(lambda)'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'weights'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Lasso and Elastic-Net Paths'</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">l1</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">l2</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="s">'Lasso'</span><span class="p">,</span> <span class="s">'Elastic-Net'</span><span class="p">),</span> <span class="n">loc</span><span class="o">=</span><span class="s">'lower left'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'tight'</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> </div> </div> </div> </div> </div> <div class="clearer"></div> </div> </div> <div class="footer"> <p style="text-align: center">This documentation is relative to scikits.learn 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