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<div class="section" id="sgd-convex-loss-functions">
<span id="example-linear-model-plot-sgd-loss-functions-py"></span><h1>SGD: Convex Loss Functions<a class="headerlink" href="#sgd-convex-loss-functions" title="Permalink to this headline">ΒΆ</a></h1>
<p>Plot the convex loss functions supported by <cite>scikits.learn.linear_model.stochastic_gradient</cite>.</p>
<img alt="auto_examples/linear_model/images/plot_sgd_loss_functions.png" class="align-center" src="auto_examples/linear_model/images/plot_sgd_loss_functions.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_sgd_loss_functions.py"><tt class="xref download docutils literal"><span class="pre">plot_sgd_loss_functions.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="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.sgd_fast</span> <span class="kn">import</span> <span class="n">Hinge</span><span class="p">,</span> \
<span class="n">ModifiedHuber</span><span class="p">,</span> <span class="n">SquaredLoss</span>
<span class="c">###############################################################################</span>
<span class="c"># Define loss funcitons</span>
<span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span> <span class="o">=</span> <span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span>
<span class="n">hinge</span> <span class="o">=</span> <span class="n">Hinge</span><span class="p">()</span>
<span class="n">log_loss</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">,</span> <span class="n">p</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">log2</span><span class="p">(</span><span class="mf">1.0</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">z</span><span class="p">))</span>
<span class="n">modified_huber</span> <span class="o">=</span> <span class="n">ModifiedHuber</span><span class="p">()</span>
<span class="n">squared_loss</span> <span class="o">=</span> <span class="n">SquaredLoss</span><span class="p">()</span>
<span class="c">###############################################################################</span>
<span class="c"># Plot loss funcitons</span>
<span class="n">xx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">xmin</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="s">'k-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s">"Zero-one loss"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="p">[</span><span class="n">hinge</span><span class="o">.</span><span class="n">loss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xx</span><span class="p">],</span> <span class="s">'g-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s">"Hinge loss"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="p">[</span><span class="n">log_loss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xx</span><span class="p">],</span> <span class="s">'r-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s">"Log loss"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="p">[</span><span class="n">modified_huber</span><span class="o">.</span><span class="n">loss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xx</span><span class="p">],</span> <span class="s">'y-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s">"Modified huber loss"</span><span class="p">)</span>
<span class="c">#pl.plot(xx, [2.0*squared_loss.loss(x,1) for x in xx], 'c-',</span>
<span class="c"># label="Squared loss")</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylim</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</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">loc</span><span class="o">=</span><span class="s">"upper right"</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">r"$y \cdot f(x)$"</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">"$L(y, f(x))$"</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>
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