對Keras自帶Loss Function的深入研究

更新時間：2021年05月25日 09:15:48 作者：Forskamse

這篇文章主要介紹了對Keras自帶Loss Function的深入研究，具有很好的參考價值，希望對大家有所幫助。如有錯誤或未考慮完全的地方，望不吝賜教

本文研究Keras自帶的幾個常用的Loss Function。

1. categorical_crossentropy VS. sparse_categorical_crossentropy

注意到二者的主要差別在于輸入是否為integer tensor。在文檔中，我們還可以找到關于二者如何選擇的描述：

解釋一下這里的Integer target 與 Categorical target，實際上Integer target經過獨熱編碼就變成了Categorical target，舉例說明：

(類別數5)
Integer target: [1,2,4]
Categorical target： [[0. 1. 0. 0. 0.]
					 [0. 0. 1. 0. 0.]
					 [0. 0. 0. 0. 1.]]

在Keras中提供了to_categorical方法來實現二者的轉化：

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

注意categorical_crossentropy和sparse_categorical_crossentropy的輸入參數output，都是softmax輸出的tensor。我們都知道softmax的輸出服從多項分布，

因此categorical_crossentropy和sparse_categorical_crossentropy應當應用于多分類問題。

我們再看看這兩個的源碼，來驗證一下：

https://github.com/tensorflow/tensorflow/blob/r1.13/tensorflow/python/keras/backend.py
--------------------------------------------------------------------------------------------------------------------
def categorical_crossentropy(target, output, from_logits=False, axis=-1):
  """Categorical crossentropy between an output tensor and a target tensor.
  Arguments:
      target: A tensor of the same shape as `output`.
      output: A tensor resulting from a softmax
          (unless `from_logits` is True, in which
          case `output` is expected to be the logits).
      from_logits: Boolean, whether `output` is the
          result of a softmax, or is a tensor of logits.
      axis: Int specifying the channels axis. `axis=-1` corresponds to data
          format `channels_last', and `axis=1` corresponds to data format
          `channels_first`.
  Returns:
      Output tensor.
  Raises:
      ValueError: if `axis` is neither -1 nor one of the axes of `output`.
  """
  rank = len(output.shape)
  axis = axis % rank
  # Note: nn.softmax_cross_entropy_with_logits_v2
  # expects logits, Keras expects probabilities.
  if not from_logits:
    # scale preds so that the class probas of each sample sum to 1
    output = output / math_ops.reduce_sum(output, axis, True)
    # manual computation of crossentropy
    epsilon_ = _to_tensor(epsilon(), output.dtype.base_dtype)
    output = clip_ops.clip_by_value(output, epsilon_, 1. - epsilon_)
    return -math_ops.reduce_sum(target * math_ops.log(output), axis)
  else:
    return nn.softmax_cross_entropy_with_logits_v2(labels=target, logits=output)
--------------------------------------------------------------------------------------------------------------------
def sparse_categorical_crossentropy(target, output, from_logits=False, axis=-1):
  """Categorical crossentropy with integer targets.
  Arguments:
      target: An integer tensor.
      output: A tensor resulting from a softmax
          (unless `from_logits` is True, in which
          case `output` is expected to be the logits).
      from_logits: Boolean, whether `output` is the
          result of a softmax, or is a tensor of logits.
      axis: Int specifying the channels axis. `axis=-1` corresponds to data
          format `channels_last', and `axis=1` corresponds to data format
          `channels_first`.
  Returns:
      Output tensor.
  Raises:
      ValueError: if `axis` is neither -1 nor one of the axes of `output`.
  """
  rank = len(output.shape)
  axis = axis % rank
  if axis != rank - 1:
    permutation = list(range(axis)) + list(range(axis + 1, rank)) + [axis]
    output = array_ops.transpose(output, perm=permutation)
  # Note: nn.sparse_softmax_cross_entropy_with_logits
  # expects logits, Keras expects probabilities.
  if not from_logits:
    epsilon_ = _to_tensor(epsilon(), output.dtype.base_dtype)
    output = clip_ops.clip_by_value(output, epsilon_, 1 - epsilon_)
    output = math_ops.log(output)
  output_shape = output.shape
  targets = cast(flatten(target), 'int64')
  logits = array_ops.reshape(output, [-1, int(output_shape[-1])])
  res = nn.sparse_softmax_cross_entropy_with_logits(
      labels=targets, logits=logits)
  if len(output_shape) >= 3:
    # If our output includes timesteps or spatial dimensions we need to reshape
    return array_ops.reshape(res, array_ops.shape(output)[:-1])
  else:
    return res

categorical_crossentropy計算交叉熵時使用的是nn.softmax_cross_entropy_with_logits_v2( labels=targets, logits=logits)，而sparse_categorical_crossentropy使用的是nn.sparse_softmax_cross_entropy_with_logits( labels=targets, logits=logits)，二者本質并無區(qū)別，只是對輸入參數logits的要求不同，v2要求的是logits與labels格式相同（即元素也是獨熱的），而sparse則要求logits的元素是個數值，與上面Integer format和Categorical format的對比含義類似。

綜上所述，categorical_crossentropy和sparse_categorical_crossentropy只不過是輸入參數target類型上的區(qū)別，其loss的計算在本質上沒有區(qū)別，就是交叉熵；二者是針對多分類（Multi-class）任務的。

2. Binary_crossentropy

二元交叉熵，從名字中我們可以看出，這個loss function可能是適用于二分類的。文檔中并沒有詳細說明，那么直接看看源碼吧：

https://github.com/tensorflow/tensorflow/blob/r1.13/tensorflow/python/keras/backend.py
--------------------------------------------------------------------------------------------------------------------
def binary_crossentropy(target, output, from_logits=False):
  """Binary crossentropy between an output tensor and a target tensor.
  Arguments:
      target: A tensor with the same shape as `output`.
      output: A tensor.
      from_logits: Whether `output` is expected to be a logits tensor.
          By default, we consider that `output`
          encodes a probability distribution.
  Returns:
      A tensor.
  """
  # Note: nn.sigmoid_cross_entropy_with_logits
  # expects logits, Keras expects probabilities.
  if not from_logits:
    # transform back to logits
    epsilon_ = _to_tensor(epsilon(), output.dtype.base_dtype)
    output = clip_ops.clip_by_value(output, epsilon_, 1 - epsilon_)
    output = math_ops.log(output / (1 - output))
  return nn.sigmoid_cross_entropy_with_logits(labels=target, logits=output)

可以看到源碼中計算使用了nn.sigmoid_cross_entropy_with_logits，熟悉tensorflow的應該比較熟悉這個損失函數了，它可以用于簡單的二分類，也可以用于多標簽任務，而且應用廣泛，在樣本合理的情況下（如不存在類別不均衡等問題）的情況下，通?？梢灾苯邮褂谩?/p>

補充：keras自定義loss function的簡單方法

首先看一下Keras中我們常用到的目標函數（如mse,mae等）是如何定義的

from keras import backend as K
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(), np.inf))
    return 100. * K.mean(diff, axis=-1)
def categorical_crossentropy(y_true, y_pred):
    '''Expects a binary class matrix instead of a vector of scalar classes.
    '''
    return K.categorical_crossentropy(y_pred, y_true)
def sparse_categorical_crossentropy(y_true, y_pred):
    '''expects an array of integer classes.
    Note: labels shape must have the same number of dimensions as output shape.
    If you get a shape error, add a length-1 dimension to labels.
    '''
    return K.sparse_categorical_crossentropy(y_pred, y_true)
def binary_crossentropy(y_true, y_pred):
    return K.mean(K.binary_crossentropy(y_pred, y_true), 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.mean(y_true * y_pred, axis=-1)

所以仿照以上的方法，可以自己定義特定任務的目標函數。比如：定義預測值與真實值的差

from keras import backend as K
def new_loss(y_true,y_pred):
    return K.mean((y_pred-y_true),axis = -1)

然后，應用你自己定義的目標函數進行編譯

from keras import backend as K
def my_loss(y_true,y_pred):
    return K.mean((y_pred-y_true),axis = -1)
model.compile(optimizer=optimizers.RMSprop(lr)，loss=my_loss,
metrics=['accuracy'])

以上為個人經驗，希望能給大家一個參考，也希望大家多多支持腳本之家。

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