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"""Utilities for the neural network modules
"""
# Author: Issam H. Laradji <issam.laradji@gmail.com>
# License: BSD 3 clause
import numpy as np
from scipy.special import expit as logistic_sigmoid
def identity(X):
"""Simply return the input array.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Data, where n_samples is the number of samples
and n_features is the number of features.
Returns
-------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Same as the input data.
"""
return X
def logistic(X):
"""Compute the logistic function inplace.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
The transformed data.
"""
return logistic_sigmoid(X, out=X)
def tanh(X):
"""Compute the hyperbolic tan function inplace.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
The transformed data.
"""
return np.tanh(X, out=X)
def relu(X):
"""Compute the rectified linear unit function inplace.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
The transformed data.
"""
np.clip(X, 0, np.finfo(X.dtype).max, out=X)
return X
def softmax(X):
"""Compute the K-way softmax function inplace.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
The transformed data.
"""
tmp = X - X.max(axis=1)[:, np.newaxis]
np.exp(tmp, out=X)
X /= X.sum(axis=1)[:, np.newaxis]
return X
ACTIVATIONS = {'identity': identity, 'tanh': tanh, 'logistic': logistic,
'relu': relu, 'softmax': softmax}
def inplace_identity_derivative(Z, delta):
"""Apply the derivative of the identity function: do nothing.
Parameters
----------
Z : {array-like, sparse matrix}, shape (n_samples, n_features)
The data which was output from the identity activation function during
the forward pass.
delta : {array-like}, shape (n_samples, n_features)
The backpropagated error signal to be modified inplace.
"""
# Nothing to do
def inplace_logistic_derivative(Z, delta):
"""Apply the derivative of the logistic sigmoid function.
It exploits the fact that the derivative is a simple function of the output
value from logistic function.
Parameters
----------
Z : {array-like, sparse matrix}, shape (n_samples, n_features)
The data which was output from the logistic activation function during
the forward pass.
delta : {array-like}, shape (n_samples, n_features)
The backpropagated error signal to be modified inplace.
"""
delta *= Z
delta *= (1 - Z)
def inplace_tanh_derivative(Z, delta):
"""Apply the derivative of the hyperbolic tanh function.
It exploits the fact that the derivative is a simple function of the output
value from hyperbolic tangent.
Parameters
----------
Z : {array-like, sparse matrix}, shape (n_samples, n_features)
The data which was output from the hyperbolic tangent activation
function during the forward pass.
delta : {array-like}, shape (n_samples, n_features)
The backpropagated error signal to be modified inplace.
"""
delta *= (1 - Z ** 2)
def inplace_relu_derivative(Z, delta):
"""Apply the derivative of the relu function.
It exploits the fact that the derivative is a simple function of the output
value from rectified linear units activation function.
Parameters
----------
Z : {array-like, sparse matrix}, shape (n_samples, n_features)
The data which was output from the rectified linear units activation
function during the forward pass.
delta : {array-like}, shape (n_samples, n_features)
The backpropagated error signal to be modified inplace.
"""
delta[Z == 0] = 0
DERIVATIVES = {'identity': inplace_identity_derivative,
'tanh': inplace_tanh_derivative,
'logistic': inplace_logistic_derivative,
'relu': inplace_relu_derivative}
def squared_loss(y_true, y_pred):
"""Compute the squared loss for regression.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) values.
y_pred : array-like or label indicator matrix
Predicted values, as returned by a regression estimator.
Returns
-------
loss : float
The degree to which the samples are correctly predicted.
"""
return ((y_true - y_pred) ** 2).mean() / 2
def log_loss(y_true, y_prob):
"""Compute Logistic loss for classification.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) labels.
y_prob : array-like of float, shape = (n_samples, n_classes)
Predicted probabilities, as returned by a classifier's
predict_proba method.
Returns
-------
loss : float
The degree to which the samples are correctly predicted.
"""
y_prob = np.clip(y_prob, 1e-10, 1 - 1e-10)
if y_prob.shape[1] == 1:
y_prob = np.append(1 - y_prob, y_prob, axis=1)
if y_true.shape[1] == 1:
y_true = np.append(1 - y_true, y_true, axis=1)
return -np.sum(y_true * np.log(y_prob)) / y_prob.shape[0]
def binary_log_loss(y_true, y_prob):
"""Compute binary logistic loss for classification.
This is identical to log_loss in binary classification case,
but is kept for its use in multilabel case.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) labels.
y_prob : array-like of float, shape = (n_samples, n_classes)
Predicted probabilities, as returned by a classifier's
predict_proba method.
Returns
-------
loss : float
The degree to which the samples are correctly predicted.
"""
y_prob = np.clip(y_prob, 1e-10, 1 - 1e-10)
return -np.sum(y_true * np.log(y_prob) +
(1 - y_true) * np.log(1 - y_prob)) / y_prob.shape[0]
LOSS_FUNCTIONS = {'squared_loss': squared_loss, 'log_loss': log_loss,
'binary_log_loss': binary_log_loss}
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