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<h2 id="usage-of-loss-functions">Usage of loss functions</h2>
<p>A loss function (or objective function, or optimization score function) is one of the two parameters required to compile a model:</p>
<pre><code class="python">model.compile(loss='mean_squared_error', optimizer='sgd')
</code></pre>
<pre><code class="python">from keras import losses
model.compile(loss=losses.mean_squared_error, optimizer='sgd')
</code></pre>
<p>You can either pass the name of an existing loss function, or pass a TensorFlow/Theano symbolic function that returns a scalar for each data-point and takes the following two arguments:</p>
<ul>
<li><strong>y_true</strong>: True labels. TensorFlow/Theano tensor.</li>
<li><strong>y_pred</strong>: Predictions. TensorFlow/Theano tensor of the same shape as y_true.</li>
</ul>
<p>The actual optimized objective is the mean of the output array across all datapoints.</p>
<p>For a few examples of such functions, check out the <a href="https://github.com/keras-team/keras/blob/master/keras/losses.py">losses source</a>.</p>
<h2 id="available-loss-functions">Available loss functions</h2>
<h3 id="mean_squared_error">mean_squared_error</h3>
<pre><code class="python">keras.losses.mean_squared_error(y_true, y_pred)
</code></pre>
<hr />
<h3 id="mean_absolute_error">mean_absolute_error</h3>
<pre><code class="python">keras.losses.mean_absolute_error(y_true, y_pred)
</code></pre>
<hr />
<h3 id="mean_absolute_percentage_error">mean_absolute_percentage_error</h3>
<pre><code class="python">keras.losses.mean_absolute_percentage_error(y_true, y_pred)
</code></pre>
<hr />
<h3 id="mean_squared_logarithmic_error">mean_squared_logarithmic_error</h3>
<pre><code class="python">keras.losses.mean_squared_logarithmic_error(y_true, y_pred)
</code></pre>
<hr />
<h3 id="squared_hinge">squared_hinge</h3>
<pre><code class="python">keras.losses.squared_hinge(y_true, y_pred)
</code></pre>
<hr />
<h3 id="hinge">hinge</h3>
<pre><code class="python">keras.losses.hinge(y_true, y_pred)
</code></pre>
<hr />
<h3 id="categorical_hinge">categorical_hinge</h3>
<pre><code class="python">keras.losses.categorical_hinge(y_true, y_pred)
</code></pre>
<hr />
<h3 id="logcosh">logcosh</h3>
<pre><code class="python">keras.losses.logcosh(y_true, y_pred)
</code></pre>
<p>Logarithm of the hyperbolic cosine of the prediction error.</p>
<p><code>log(cosh(x))</code> is approximately equal to <code>(x ** 2) / 2</code> for small <code>x</code> and
to <code>abs(x) - log(2)</code> for large <code>x</code>. This means that 'logcosh' works mostly
like the mean squared error, but will not be so strongly affected by the
occasional wildly incorrect prediction.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>y_true</strong>: tensor of true targets.</li>
<li><strong>y_pred</strong>: tensor of predicted targets.</li>
</ul>
<p><strong>Returns</strong></p>
<p>Tensor with one scalar loss entry per sample.</p>
<hr />
<h3 id="huber_loss">huber_loss</h3>
<pre><code class="python">keras.losses.huber_loss(y_true, y_pred, delta=1.0)
</code></pre>
<hr />
<h3 id="categorical_crossentropy">categorical_crossentropy</h3>
<pre><code class="python">keras.losses.categorical_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)
</code></pre>
<hr />
<h3 id="sparse_categorical_crossentropy">sparse_categorical_crossentropy</h3>
<pre><code class="python">keras.losses.sparse_categorical_crossentropy(y_true, y_pred, from_logits=False, axis=-1)
</code></pre>
<hr />
<h3 id="binary_crossentropy">binary_crossentropy</h3>
<pre><code class="python">keras.losses.binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)
</code></pre>
<hr />
<h3 id="kullback_leibler_divergence">kullback_leibler_divergence</h3>
<pre><code class="python">keras.losses.kullback_leibler_divergence(y_true, y_pred)
</code></pre>
<hr />
<h3 id="poisson">poisson</h3>
<pre><code class="python">keras.losses.poisson(y_true, y_pred)
</code></pre>
<hr />
<h3 id="cosine_proximity">cosine_proximity</h3>
<pre><code class="python">keras.losses.cosine_proximity(y_true, y_pred, axis=-1)
</code></pre>
<hr />
<h3 id="is_categorical_crossentropy">is_categorical_crossentropy</h3>
<pre><code class="python">keras.losses.is_categorical_crossentropy(loss)
</code></pre>
<hr />
<p><strong>Note</strong>: when using the <code>categorical_crossentropy</code> loss, your targets should be in categorical format (e.g. if you have 10 classes, the target for each sample should be a 10-dimensional vector that is all-zeros except for a 1 at the index corresponding to the class of the sample). In order to convert <em>integer targets</em> into <em>categorical targets</em>, you can use the Keras utility <code>to_categorical</code>:</p>
<pre><code class="python">from keras.utils import to_categorical
categorical_labels = to_categorical(int_labels, num_classes=None)
</code></pre>
<p>When using the <code>sparse_categorical_crossentropy</code> loss, your targets should be <em>integer targets</em>.
If you have categorical targets, you should use <code>categorical_crossentropy</code>.</p>
<p><code>categorical_crossentropy</code> is another term for <a href="http://wiki.fast.ai/index.php/Log_Loss">multi-class log loss</a>. </p>
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