keras损失函数详解

以下信息均来自官网

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损失函数的使用

损失函数（或称目标函数、优化评分函数）是编译模型时所需的两个参数之一：

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

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

你可以传递一个现有的损失函数名，或者一个 TensorFlow/Theano 符号函数。 该符号函数为每个数据点返回一个标量，有以下两个参数:

• y_true: 真实标签。TensorFlow/Theano 张量。
• y_pred: 预测值。TensorFlow/Theano 张量，其 shape 与 y_true 相同。

实际的优化目标是所有数据点的输出数组的平均值。

可用损失函数

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)

预测误差的双曲余弦的对数。

对于小的 x，log(cosh(x)) 近似等于 (x ** 2) / 2。对于大的 x，近似于 abs(x) - log(2)。这表示 'logcosh' 与均方误差大致相同，但是不会受到偶尔疯狂的错误预测的强烈影响。

参数

• y_true: 目标真实值的张量。
• y_pred: 目标预测值的张量。

返回

每个样本都有一个标量损失的张量。

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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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注意: 当使用 categorical_crossentropy 损失时，你的目标值应该是分类格式 (即，如果你有 10 个类，每个样本的目标值应该是一个 10 维的向量，这个向量除了表示类别的那个索引为 1，其他均为 0)。 为了将 整数目标值 转换为 分类目标值，你可以使用 Keras 实用函数 to_categorical：

from keras.utils.np_utils import to_categorical

categorical_labels = to_categorical(int_labels, num_classes=None)

如果还不明白，请看下面的源码

 """Built-in loss functions.
 """
 from __future__ import absolute_import
 from __future__ import division
 from __future__ import print_function

 import six
 from . import backend as K
 from .utils.generic_utils import deserialize_keras_object
 from .utils.generic_utils import serialize_keras_object

 def mean_squared_error(y_true, y_pred):
     return K.mean(K.square(y_pred - y_true), axis=-1)

 def mean_absolute_error(y_true, y_pred):
     return K.mean(K.abs(y_pred - y_true), axis=-1)

 def mean_absolute_percentage_error(y_true, y_pred):
     diff = K.abs((y_true - y_pred) / K.clip(K.abs(y_true),
                                             K.epsilon(),
                                             None))
     return 100. * K.mean(diff, axis=-1)

 def mean_squared_logarithmic_error(y_true, y_pred):
     first_log = K.log(K.clip(y_pred, K.epsilon(), None) + 1.)
     second_log = K.log(K.clip(y_true, K.epsilon(), None) + 1.)
     return K.mean(K.square(first_log - second_log), axis=-1)

 def squared_hinge(y_true, y_pred):
     return K.mean(K.square(K.maximum(1. - y_true * y_pred, 0.)), axis=-1)

 def hinge(y_true, y_pred):
     return K.mean(K.maximum(1. - y_true * y_pred, 0.), axis=-1)

 def categorical_hinge(y_true, y_pred):
     pos = K.sum(y_true * y_pred, axis=-1)
     neg = K.max((1. - y_true) * y_pred, axis=-1)
     return K.maximum(0., neg - pos + 1.)

 def 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.
     """
     def _logcosh(x):
         return x + K.softplus(-2. * x) - K.log(2.)
     return K.mean(_logcosh(y_pred - y_true), axis=-1)

 def categorical_crossentropy(y_true, y_pred):
     return K.categorical_crossentropy(y_true, y_pred)

 def sparse_categorical_crossentropy(y_true, y_pred):
     return K.sparse_categorical_crossentropy(y_true, y_pred)

 def binary_crossentropy(y_true, y_pred):
     return K.mean(K.binary_crossentropy(y_true, y_pred), axis=-1)

 def kullback_leibler_divergence(y_true, y_pred):
     y_true = K.clip(y_true, K.epsilon(), 1)
     y_pred = K.clip(y_pred, K.epsilon(), 1)
     return K.sum(y_true * K.log(y_true / y_pred), axis=-1)

 def poisson(y_true, y_pred):
     return K.mean(y_pred - y_true * K.log(y_pred + K.epsilon()), axis=-1)

 def cosine_proximity(y_true, y_pred):
     y_true = K.l2_normalize(y_true, axis=-1)
     y_pred = K.l2_normalize(y_pred, axis=-1)
     return -K.sum(y_true * y_pred, axis=-1)

 # Aliases.

 mse = MSE = mean_squared_error
 mae = MAE = mean_absolute_error
 mape = MAPE = mean_absolute_percentage_error
 msle = MSLE = mean_squared_logarithmic_error
 kld = KLD = kullback_leibler_divergence
 cosine = cosine_proximity

 def serialize(loss):
     return serialize_keras_object(loss)

 def deserialize(name, custom_objects=None):
     return deserialize_keras_object(name,
                                     module_objects=globals(),
                                     custom_objects=custom_objects,
                                     printable_module_name='loss function')

 def get(identifier):
     """Get the `identifier` loss function.
     # Arguments
         identifier: None or str, name of the function.
     # Returns
         The loss function or None if `identifier` is None.
     # Raises
         ValueError if unknown identifier.
     """
     if identifier is None:
         return None
     if isinstance(identifier, six.string_types):
         identifier = str(identifier)
         return deserialize(identifier)
     if isinstance(identifier, dict):
         return deserialize(identifier)
     elif callable(identifier):
         return identifier
     else:
         raise ValueError('Could not interpret '
                          'loss function identifier:', identifier)