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.

Arguments

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

Returns

Tensor with one scalar loss entry per sample.

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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 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.np_utils import to_categorical

categorical_labels = to_categorical(int_labels, num_classes=None)