losses.py

"""
Define our custom loss function.
"""
from keras import backend as K
import tensorflow as tf

import dill


def binary_focal_loss(gamma=2., alpha=.25):
    """
    Binary form of focal loss.

      FL(p_t) = -alpha * (1 - p_t)**gamma * log(p_t)

      where p = sigmoid(x), p_t = p or 1 - p depending on if the label is 1 or 0, respectively.

    References:
        https://arxiv.org/pdf/1708.02002.pdf
    Usage:
     model.compile(loss=[binary_focal_loss(alpha=.25, gamma=2)], metrics=["accuracy"], optimizer=adam)

    """
    def binary_focal_loss_fixed(y_true, y_pred):
        """
        :param y_true: A tensor of the same shape as `y_pred`
        :param y_pred:  A tensor resulting from a sigmoid
        :return: Output tensor.
        """
        pt_1 = tf.where(tf.equal(y_true, 1), y_pred, tf.ones_like(y_pred))
        pt_0 = tf.where(tf.equal(y_true, 0), y_pred, tf.zeros_like(y_pred))

        epsilon = K.epsilon()
        # clip to prevent NaN's and Inf's
        pt_1 = K.clip(pt_1, epsilon, 1. - epsilon)
        pt_0 = K.clip(pt_0, epsilon, 1. - epsilon)

        return -K.sum(alpha * K.pow(1. - pt_1, gamma) * K.log(pt_1)) \
               -K.sum((1 - alpha) * K.pow(pt_0, gamma) * K.log(1. - pt_0))

    return binary_focal_loss_fixed


def categorical_focal_loss(gamma=2., alpha=.25):
    """
    Softmax version of focal loss.

           m
      FL = ∑  -alpha * (1 - p_o,c)^gamma * y_o,c * log(p_o,c)
          c=1

      where m = number of classes, c = class and o = observation

    Parameters:
      alpha -- the same as weighing factor in balanced cross entropy
      gamma -- focusing parameter for modulating factor (1-p)

    Default value:
      gamma -- 2.0 as mentioned in the paper
      alpha -- 0.25 as mentioned in the paper

    References:
        Official paper: https://arxiv.org/pdf/1708.02002.pdf
        https://www.tensorflow.org/api_docs/python/tf/keras/backend/categorical_crossentropy

    Usage:
     model.compile(loss=[categorical_focal_loss(alpha=.25, gamma=2)], metrics=["accuracy"], optimizer=adam)
    """
    def categorical_focal_loss_fixed(y_true, y_pred):
        """
        :param y_true: A tensor of the same shape as `y_pred`
        :param y_pred: A tensor resulting from a softmax
        :return: Output tensor.
        """

        # Scale predictions so that the class probas of each sample sum to 1
        y_pred /= K.sum(y_pred, axis=-1, keepdims=True)

        # Clip the prediction value to prevent NaN's and Inf's
        epsilon = K.epsilon()
        y_pred = K.clip(y_pred, epsilon, 1. - epsilon)

        # Calculate Cross Entropy
        cross_entropy = -y_true * K.log(y_pred)

        # Calculate Focal Loss
        loss = alpha * K.pow(1 - y_pred, gamma) * cross_entropy

        # Sum the losses in mini_batch
        return K.sum(loss, axis=1)

    return categorical_focal_loss_fixed


if __name__ == '__main__':

    # Test serialization of nested functions
    bin_inner = dill.loads(dill.dumps(binary_focal_loss(gamma=2., alpha=.25)))
    print(bin_inner)

    cat_inner = dill.loads(dill.dumps(categorical_focal_loss(gamma=2., alpha=.25)))
    print(cat_inner)