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internal" href="#">Lasso on dense and sparse data</a></li> </ul> </div> <div class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="lasso-on-dense-and-sparse-data"> <span id="example-linear-model-lasso-dense-vs-sparse-data-py"></span><h1>Lasso on dense and sparse data<a class="headerlink" href="#lasso-on-dense-and-sparse-data" title="Permalink to this headline">ΒΆ</a></h1> <p>We show that linear_model.Lasso and linear_model.sparse.Lasso provide the same results and that in the case of sparse data linear_model.sparse.Lasso improves the speed.</p> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/lasso_dense_vs_sparse_data.py"><tt class="xref download docutils literal"><span class="pre">lasso_dense_vs_sparse_data.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">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">sparse</span> <span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="kn">from</span> <span class="nn">scikits.learn.linear_model.sparse</span> <span class="kn">import</span> <span class="n">Lasso</span> <span class="k">as</span> <span class="n">SparseLasso</span> <span class="kn">from</span> <span class="nn">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">Lasso</span> <span class="k">as</span> <span class="n">DenseLasso</span> <span class="c">###############################################################################</span> <span class="c"># The two Lasso implementations on Dense data</span> <span class="k">print</span> <span class="s">"--- Dense matrices"</span> <span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">10000</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">0</span><span class="p">)</span> <span class="n">y</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">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">alpha</span> <span class="o">=</span> <span class="mi">1</span> <span class="n">sparse_lasso</span> <span class="o">=</span> <span class="n">SparseLasso</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">alpha</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">dense_lasso</span> <span class="o">=</span> <span class="n">DenseLasso</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">alpha</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">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span> <span class="n">sparse_lasso</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">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Sparse Lasso done in </span><span class="si">%f</span><span class="s">s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span> <span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span> <span class="n">dense_lasso</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">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Dense Lasso done in </span><span class="si">%f</span><span class="s">s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Distance between coefficients : </span><span class="si">%s</span><span class="s">"</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">sparse_lasso</span><span class="o">.</span><span class="n">coef_</span> <span class="o">-</span> <span class="n">dense_lasso</span><span class="o">.</span><span class="n">coef_</span><span class="p">)</span> <span class="c">###############################################################################</span> <span class="c"># The two Lasso implementations on Sparse data</span> <span class="k">print</span> <span class="s">"--- Sparse matrices"</span> <span class="n">Xs</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <span class="n">Xs</span><span class="p">[</span><span class="n">Xs</span> <span class="o"><</span> <span class="mf">2.5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">Xs</span> <span class="o">=</span> <span class="n">sparse</span><span class="o">.</span><span class="n">coo_matrix</span><span class="p">(</span><span class="n">Xs</span><span class="p">)</span> <span class="n">Xs</span> <span class="o">=</span> <span class="n">Xs</span><span class="o">.</span><span class="n">tocsc</span><span class="p">()</span> <span class="k">print</span> <span class="s">"Matrix density : </span><span class="si">%s</span><span class="s"> </span><span class="si">%%</span><span class="s">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">Xs</span><span class="o">.</span><span class="n">nnz</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">size</span><span class="p">)</span> <span class="o">*</span> <span class="mi">100</span><span class="p">)</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="n">sparse_lasso</span> <span class="o">=</span> <span class="n">SparseLasso</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">alpha</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">dense_lasso</span> <span class="o">=</span> <span class="n">DenseLasso</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="n">alpha</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">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span> <span class="n">sparse_lasso</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">Xs</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Sparse Lasso done in </span><span class="si">%f</span><span class="s">s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span> <span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span> <span class="n">dense_lasso</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">Xs</span><span class="o">.</span><span class="n">todense</span><span class="p">(),</span> <span class="n">y</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Dense Lasso done in </span><span class="si">%f</span><span class="s">s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span> <span class="k">print</span> <span class="s">"Distance between coefficients : </span><span class="si">%s</span><span class="s">"</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">sparse_lasso</span><span class="o">.</span><span class="n">coef_</span> <span class="o">-</span> <span class="n">dense_lasso</span><span class="o">.</span><span class="n">coef_</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 version 0.6.0<p> © 2010, scikits.learn developers (BSD Lincense). 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