keras損失函數詳解

以下信息均來自官網

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損失函數的使用

損失函數（或稱目標函數、優化評分函數）是編譯模型時所需的兩個參數之一：

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

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

 

你可以傳遞一個現有的損失函數名，或者一個 TensorFlow/Theano 符號函數。 該符號函數為每個數據點返回一個標量，有以下兩個參數:

• y_true: 真實標簽。TensorFlow/Theano 張量。
• y_pred: 預測值。TensorFlow/Theano 張量，其 shape 與 y_true 相同。

實際的優化目標是所有數據點的輸出數組的平均值。

可用損失函數

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)

---

hinge

hinge(y_true, y_pred)

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categorical_hinge

categorical_hinge(y_true, y_pred)

---

logcosh

logcosh(y_true, y_pred)

預測誤差的雙曲余弦的對數。

對於小的 x，log(cosh(x)) 近似等於 (x ** 2) / 2。對於大的 x，近似於 abs(x) - log(2)。這表示 'logcosh' 與均方誤差大致相同，但是不會受到偶爾瘋狂的錯誤預測的強烈影響。

參數

• y_true: 目標真實值的張量。
• y_pred: 目標預測值的張量。

返回

每個樣本都有一個標量損失的張量。

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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)

---

poisson

poisson(y_true, y_pred)

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cosine_proximity

cosine_proximity(y_true, y_pred)

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注意: 當使用 categorical_crossentropy 損失時，你的目標值應該是分類格式 (即，如果你有 10 個類，每個樣本的目標值應該是一個 10 維的向量，這個向量除了表示類別的那個索引為 1，其他均為 0)。 為了將 整數目標值 轉換為 分類目標值，你可以使用 Keras 實用函數 to_categorical：

from keras.utils.np_utils import to_categorical categorical_labels = to_categorical(int_labels, num_classes=None)

如果還不明白，請看下面的源碼

"""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)