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

mean_squared_error(y_true, y_pred)

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mean_absolute_error

mean_absolute_error(y_true, y_pred)

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mean_absolute_percentage_error

mean_absolute_percentage_error(y_true, y_pred)

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mean_squared_logarithmic_error

mean_squared_logarithmic_error(y_true, y_pred)

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squared_hinge

squared_hinge(y_true, y_pred)

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hinge

hinge(y_true, y_pred)

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categorical_hinge

categorical_hinge(y_true, y_pred)

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logcosh

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. However, it may return NaNs if the intermediate value cosh(y_pred - y_true) is too large to be represented in the chosen precision.

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categorical_crossentropy

categorical_crossentropy(y_true, y_pred)

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sparse_categorical_crossentropy

sparse_categorical_crossentropy(y_true, y_pred)

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binary_crossentropy

binary_crossentropy(y_true, y_pred)

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kullback_leibler_divergence

kullback_leibler_divergence(y_true, y_pred)

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poisson

poisson(y_true, y_pred)

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cosine_proximity

cosine_proximity(y_true, y_pred)

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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 expect 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.np_utils import to_categorical

categorical_labels = to_categorical(int_labels, num_classes=None)