#!/usr/bin/env python3
# coding: utf-8
"""
Created in April 2022
@author: Simon Delarue <sdelarue@enst.fr>
@author: Thomas Bonald <bonald@enst.fr>
"""
from typing import Union
import numpy as np
from sknetwork.gnn.base_activation import BaseLoss
from sknetwork.gnn.activation import Sigmoid, Softmax
[docs]class CrossEntropy(BaseLoss, Softmax):
"""Cross entropy loss with softmax activation.
For a single sample with value :math:`x` and true label :math:`y`, the cross-entropy loss
is:
:math:`-\\sum_i 1_{\\{y=i\\}} \\log (p_i)`
with
:math:`p_i = e^{x_i} / \\sum_j e^{x_j}`.
For :math:`n` samples, return the average loss.
"""
def __init__(self):
super(CrossEntropy, self).__init__()
self.name = 'Cross entropy'
[docs] @staticmethod
def loss(signal: np.ndarray, labels: np.ndarray) -> float:
"""Get loss value.
Parameters
----------
signal : np.ndarray, shape (n_samples, n_channels)
Input signal (before activation).
The number of channels must be at least 2.
labels : np.ndarray, shape (n_samples)
True labels.
Returns
-------
value : float
Loss value.
"""
n = len(labels)
probs = Softmax.output(signal)
# for numerical stability
eps = 1e-10
probs = np.clip(probs, eps, 1 - eps)
value = -np.log(probs[np.arange(n), labels]).sum()
return value / n
[docs] @staticmethod
def loss_gradient(signal: np.ndarray, labels: np.ndarray) -> np.ndarray:
"""Get the gradient of the loss function (including activation).
Parameters
----------
signal : np.ndarray, shape (n_samples, n_channels)
Input signal (before activation).
labels : np.ndarray, shape (n_samples)
True labels.
Returns
-------
gradient: float
Gradient of the loss function.
"""
probs = Softmax.output(signal)
one_hot_encoding = np.zeros_like(probs)
one_hot_encoding[np.arange(len(labels)), labels] = 1
gradient = probs - one_hot_encoding
return gradient
[docs]class BinaryCrossEntropy(BaseLoss, Sigmoid):
"""Binary cross entropy loss with sigmoid activation.
For a single sample with true label :math:`y` and predicted probability :math:`p`, the binary cross-entropy loss
is:
:math:`-y \\log (p) - (1-y) \\log (1 - p).`
For :math:`n` samples, return the average loss.
"""
def __init__(self):
super(BinaryCrossEntropy, self).__init__()
self.name = 'Binary cross entropy'
[docs] @staticmethod
def loss(signal: np.ndarray, labels: np.ndarray) -> float:
"""Get loss value.
Parameters
----------
signal : np.ndarray, shape (n_samples, n_channels)
Input signal (before activation).
The number of channels must be at least 2.
labels : np.ndarray, shape (n_samples)
True labels.
Returns
-------
value : float
Loss value.
"""
probs = Sigmoid.output(signal)
n = len(labels)
# for numerical stability
eps = 1e-15
probs = np.clip(probs, eps, 1 - eps)
if probs.shape[1] == 1:
# binary labels
value = -np.log(probs[labels > 0]).sum()
value -= np.log((1 - probs)[labels == 0]).sum()
else:
# general case
value = -np.log(1 - probs)
value[np.arange(n), labels] = -np.log(probs[np.arange(n), labels])
value = value.sum()
return value / n
[docs] @staticmethod
def loss_gradient(signal: np.ndarray, labels: np.ndarray) -> np.ndarray:
"""Get the gradient of the loss function (including activation).
Parameters
----------
signal : np.ndarray, shape (n_samples, n_channels)
Input signal (before activation).
labels : np.ndarray, shape (n_samples)
True labels.
Returns
-------
gradient: float
Gradient of the loss function.
"""
probs = Sigmoid.output(signal)
gradient = (probs.T - labels).T
return gradient
def get_loss(loss: Union[BaseLoss, str] = 'CrossEntropyLoss') -> BaseLoss:
"""Instantiate loss function according to parameters.
Parameters
----------
loss : str or loss function.
Which loss function to use. Can be ``'CrossEntropy'`` or ``'BinaryCrossEntropy'`` or custom loss.
Returns
-------
Loss function object.
"""
if issubclass(type(loss), BaseLoss):
return loss
elif type(loss) == str:
loss = loss.lower().replace(' ', '')
if loss in ['crossentropy', 'ce']:
return CrossEntropy()
elif loss in ['binarycrossentropy', 'bce']:
return BinaryCrossEntropy()
else:
raise ValueError("Loss must be either \"CrossEntropy\" or \"BinaryCrossEntropy\".")
else:
raise TypeError("Loss must be either an \"BaseLoss\" object or a string.")