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<h3>Contents</h3>
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<li><a class="reference internal" href="#">Lasso parameter estimation with path and cross-validation</a></li>
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<div class="section" id="lasso-parameter-estimation-with-path-and-cross-validation">
<span id="example-linear-model-lasso-path-with-crossvalidation-py"></span><h1>Lasso parameter estimation with path and cross-validation<a class="headerlink" href="#lasso-parameter-estimation-with-path-and-cross-validation" title="Permalink to this headline">ΒΆ</a></h1>
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/lasso_path_with_crossvalidation.py"><tt class="xref download docutils literal"><span class="pre">lasso_path_with_crossvalidation.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="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="c">################################################################################</span>
<span class="c"># generate some sparse data to play with</span>
<span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">100</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span><span class="p">)</span>
<span class="n">coef</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_features</span><span class="p">)</span>
<span class="n">coef</span><span class="p">[</span><span class="mi">10</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">0</span> <span class="c"># sparsify coef</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">coef</span><span class="p">)</span>
<span class="c"># add noise</span>
<span class="n">y</span> <span class="o">+=</span> <span class="mf">0.01</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">((</span><span class="n">n_samples</span><span class="p">,))</span>
<span class="c"># Split data in train set and test set</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="n">n_samples</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">n_samples</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span>
<span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">n_samples</span><span class="o">/</span><span class="mi">2</span><span class="p">:],</span> <span class="n">y</span><span class="p">[</span><span class="n">n_samples</span><span class="o">/</span><span class="mi">2</span><span class="p">:]</span>
<span class="c">################################################################################</span>
<span class="c"># Lasso with path and cross-validation using LassoCV path</span>
<span class="kn">from</span> <span class="nn">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">LassoCV</span>
<span class="kn">from</span> <span class="nn">scikits.learn.cross_val</span> <span class="kn">import</span> <span class="n">KFold</span>
<span class="n">cv</span> <span class="o">=</span> <span class="n">KFold</span><span class="p">(</span><span class="n">n_samples</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">lasso_cv</span> <span class="o">=</span> <span class="n">LassoCV</span><span class="p">()</span>
<span class="c"># fit_params = {'max_iter':100}</span>
<span class="n">y_</span> <span class="o">=</span> <span class="n">lasso_cv</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">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">)</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="k">print</span> <span class="s">"Optimal regularization parameter = </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">lasso_cv</span><span class="o">.</span><span class="n">alpha</span>
<span class="c"># Compute explained variance on test data</span>
<span class="k">print</span> <span class="s">"r^2 on test data : </span><span class="si">%f</span><span class="s">"</span> <span class="o">%</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">y_test</span> <span class="o">-</span> <span class="n">y_</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">y_test</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
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