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<div class="section" id="log-loss">
<span id="sk-log-doc"></span><h1>log_loss<a class="headerlink" href="#log-loss" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="pai4sk.metrics.log_loss">
<code class="descclassname">pai4sk.metrics.</code><code class="descname">log_loss</code><span class="sig-paren">(</span><em>y_true</em>, <em>y_pred</em>, <em>eps=1e-15</em>, <em>normalize=True</em>, <em>sample_weight=None</em>, <em>labels=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.metrics.log_loss" title="Permalink to this definition">¶</a></dt>
<dd><p>Log loss, aka logistic loss or cross-entropy loss.</p>
<p>This is the loss function used in (multinomial) logistic regression
and extensions of it such as neural networks, defined as the negative
log-likelihood of the true labels given a probabilistic classifier’s
predictions. The log loss is only defined for two or more labels.
For a single sample with true label yt in {0,1} and
estimated probability yp that yt = 1, the log loss is</p>
<blockquote>
<div>-log P(yt|yp) = -(yt log(yp) + (1 - yt) log(1 - yp))</div></blockquote>
<p>For SnapML solver this supports both local and distributed(MPI) method of execution.</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>y_true</strong> (<em>array-like</em><em> or </em><em>label indicator matrix</em>) – Ground truth (correct) labels for n_samples samples.
It also accepts SnapML data partition, which includes the correct labels.</li>
<li><strong>y_pred</strong> (<em>array-like of float</em><em>, </em><em>shape =</em><em> (</em><em>n_samples</em><em>, </em><em>n_classes</em><em>) or </em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – Predicted probabilities, as returned by a classifier’s
predict_proba method. If <code class="docutils literal notranslate"><span class="pre">y_pred.shape</span> <span class="pre">=</span> <span class="pre">(n_samples,)</span></code>
the probabilities provided are assumed to be that of the
positive class. The labels in <code class="docutils literal notranslate"><span class="pre">y_pred</span></code> are assumed to be
ordered alphabetically, as done by
<code class="xref py py-class docutils literal notranslate"><span class="pre">preprocessing.LabelBinarizer</span></code>.</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – Log loss is undefined for p=0 or p=1, so probabilities are
clipped to max(eps, min(1 - eps, p)).</li>
<li><strong>normalize</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>optional</em><em> (</em><em>default=True</em><em>)</em>) – If true, return the mean loss per sample.
Otherwise, return the sum of the per-sample losses.</li>
<li><strong>sample_weight</strong> (<em>array-like of shape =</em><em> [</em><em>n_samples</em><em>]</em><em>, </em><em>optional</em>) – Sample weights.</li>
<li><strong>labels</strong> (<em>array-like</em><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – If not provided, labels will be inferred from y_true. If <code class="docutils literal notranslate"><span class="pre">labels</span></code>
is <code class="docutils literal notranslate"><span class="pre">None</span></code> and <code class="docutils literal notranslate"><span class="pre">y_pred</span></code> has shape (n_samples,) the labels are
assumed to be binary and are inferred from <code class="docutils literal notranslate"><span class="pre">y_true</span></code>.
.. versionadded:: 0.18</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>loss</strong></p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)">float</a></p>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">log_loss</span><span class="p">([</span><span class="s2">"spam"</span><span class="p">,</span> <span class="s2">"ham"</span><span class="p">,</span> <span class="s2">"ham"</span><span class="p">,</span> <span class="s2">"spam"</span><span class="p">],</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="gp">... </span> <span class="p">[[</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="o">.</span><span class="mi">9</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">.</span><span class="mi">8</span><span class="p">,</span> <span class="o">.</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">.</span><span class="mi">35</span><span class="p">,</span> <span class="o">.</span><span class="mi">65</span><span class="p">]])</span>
<span class="go">0.21616...</span>
</pre></div>
</div>
<p class="rubric">References</p>
<p>C.M. Bishop (2006). Pattern Recognition and Machine Learning. Springer,
p. 209.</p>
<p class="rubric">Notes</p>
<p>The logarithm used is the natural logarithm (base-e).</p>
</dd></dl>
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