## Usage of loss functions

A loss function (or objective function, or optimization score function) is one of the two parameters required to compile a model:

    model.compile(loss='mean_squared_error', optimizer='sgd')

    from keras import losses

    model.compile(loss=losses.mean_squared_error, optimizer='sgd')

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:

- y_true: True labels. TensorFlow/Theano tensor.
- y_pred: Predictions. TensorFlow/Theano tensor of the same shape as y_true.

The actual optimized objective is the mean of the output array across all datapoints.

For a few examples of such functions, check out the losses source.

## Available loss functions

### mean_squared_error

    keras.losses.mean_squared_error(y_true, y_pred)

### mean_absolute_error

    keras.losses.mean_absolute_error(y_true, y_pred)

### mean_absolute_percentage_error

    keras.losses.mean_absolute_percentage_error(y_true, y_pred)

### mean_squared_logarithmic_error

    keras.losses.mean_squared_logarithmic_error(y_true, y_pred)

### squared_hinge

    keras.losses.squared_hinge(y_true, y_pred)

### hinge

    keras.losses.hinge(y_true, y_pred)

### categorical_hinge

    keras.losses.categorical_hinge(y_true, y_pred)

### logcosh

    keras.losses.logcosh(y_true, y_pred)

Logarithm of the hyperbolic cosine of the prediction error.

`log(cosh(x))` is approximately equal to `(x ** 2) / 2` for small `x` and to `abs(x) - log(2)` for large `x`. This means that 'logcosh' works mostly like the mean squared error, but will not be so strongly affected by the occasional wildly incorrect prediction.

Arguments

- y_true: tensor of true targets.
- y_pred: tensor of predicted targets.

Returns

Tensor with one scalar loss entry per sample.

### huber_loss

    keras.losses.huber_loss(y_true, y_pred, delta=1.0)

### categorical_crossentropy

    keras.losses.categorical_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)

### sparse_categorical_crossentropy

    keras.losses.sparse_categorical_crossentropy(y_true, y_pred, from_logits=False, axis=-1)

### binary_crossentropy

    keras.losses.binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)

### kullback_leibler_divergence

    keras.losses.kullback_leibler_divergence(y_true, y_pred)

### poisson

    keras.losses.poisson(y_true, y_pred)

### cosine_proximity

    keras.losses.cosine_proximity(y_true, y_pred, axis=-1)

### is_categorical_crossentropy

    keras.losses.is_categorical_crossentropy(loss)

Note: when using the `categorical_crossentropy` 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 integer targets into categorical targets, you can use the Keras utility `to_categorical`:

    from keras.utils import to_categorical

    categorical_labels = to_categorical(int_labels, num_classes=None)

When using the `sparse_categorical_crossentropy` loss, your targets should be integer targets. If you have categorical targets, you should use `categorical_crossentropy`.

`categorical_crossentropy` is another term for multi-class log loss.

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