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<li><a class="reference internal" href="#">Regularization path of L1- Logistic Regression</a></li>
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<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-linear-model-plot-logistic-path-py"><span class="std std-ref">here</span></a> to download the full example code</p>
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<div class="sphx-glr-example-title section" id="regularization-path-of-l1-logistic-regression">
<span id="sphx-glr-auto-examples-linear-model-plot-logistic-path-py"></span><h1>Regularization path of L1- Logistic Regression<a class="headerlink" href="#regularization-path-of-l1-logistic-regression" title="Permalink to this headline">¶</a></h1>
<p>Train l1-penalized logistic regression models on a binary classification
problem derived from the Iris dataset.</p>
<p>The models are ordered from strongest regularized to least regularized. The 4
coefficients of the models are collected and plotted as a “regularization
path”: on the left-hand side of the figure (strong regularizers), all the
coefficients are exactly 0. When regularization gets progressively looser,
coefficients can get non-zero values one after the other.</p>
<p>Here we choose the SAGA solver because it can efficiently optimize for the
Logistic Regression loss with a non-smooth, sparsity inducing l1 penalty.</p>
<p>Also note that we set a low value for the tolerance to make sure that the model
has converged before collecting the coefficients.</p>
<p>We also use warm_start=True which means that the coefficients of the models are
reused to initialize the next model fit to speed-up the computation of the
full-path.</p>
<img alt="../../_images/sphx_glr_plot_logistic_path_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_logistic_path_001.png" />
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>Computing regularization path ...
This took 2.008s
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Author: Alexandre Gramfort <[email protected]></span>
<span class="c1"># License: BSD 3 clause</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">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="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.l1_min_c.html#sklearn.svm.l1_min_c" title="View documentation for sklearn.svm.l1_min_c"><span class="n">l1_min_c</span></a>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="View documentation for sklearn.datasets.load_iris"><span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</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="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">X</span> <span class="o">/=</span> <span class="n">X</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="c1"># Normalize X to speed-up convergence</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Demo path functions</span>
<span class="n">cs</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.l1_min_c.html#sklearn.svm.l1_min_c" title="View documentation for sklearn.svm.l1_min_c"><span class="n">l1_min_c</span></a><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">loss</span><span class="o">=</span><span class="s1">'log'</span><span class="p">)</span> <span class="o">*</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html#numpy.logspace" title="View documentation for numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">16</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing regularization path ..."</span><span class="p">)</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">linear_model</span><span class="o">.</span><span class="n">LogisticRegression</span></a><span class="p">(</span><span class="n">penalty</span><span class="o">=</span><span class="s1">'l1'</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="s1">'saga'</span><span class="p">,</span>
<span class="n">tol</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="nb">int</span><span class="p">(</span><span class="mf">1e6</span><span class="p">),</span>
<span class="n">warm_start</span><span class="o">=</span><span class="bp">True</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">c</span> <span class="ow">in</span> <span class="n">cs</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">C</span><span class="o">=</span><span class="n">c</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="o">.</span><span class="n">ravel</span><span class="p">()</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"This took </span><span class="si">%0.3f</span><span class="s2">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">start</span><span class="p">))</span>
<span class="n">coefs_</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">coefs_</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.log10.html#numpy.log10" title="View documentation for numpy.log10"><span class="n">np</span><span class="o">.</span><span class="n">log10</span></a><span class="p">(</span><span class="n">cs</span><span class="p">),</span> <span class="n">coefs_</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'o'</span><span class="p">)</span>
<span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="View documentation for matplotlib.pyplot.ylim"><span class="n">plt</span><span class="o">.</span><span class="n">ylim</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for 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">'log(C)'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for 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">'Coefficients'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for 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">'Logistic Regression Path'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.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="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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