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# -*- coding: utf-8 -*-
"""
@file
@brief Implements a quantile non-linear regression.
"""
import numpy as np
from sklearn.base import RegressorMixin
from sklearn.utils import check_X_y, column_or_1d
from sklearn.utils.extmath import safe_sparse_dot
from sklearn.utils.validation import check_is_fitted
from sklearn.neural_network._base import DERIVATIVES, LOSS_FUNCTIONS
from sklearn.neural_network.multilayer_perceptron import BaseMultilayerPerceptron
from sklearn.metrics import mean_absolute_error
def absolute_loss(y_true, y_pred):
"""
Computes the absolute 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 np.sum(np.abs(y_true - y_pred)) / y_true.shape[0]
def float_sign(a):
"Returns 1 if *a > 0*, otherwise -1"
if a > 1e-8:
return 1.
elif a < -1e-8:
return -1.
else:
return 0.
EXTENDED_LOSS_FUNCTIONS = {'absolute_loss': absolute_loss}
DERIVATIVE_LOSS_FUNCTIONS = {'absolute_loss': np.vectorize(float_sign)}
class CustomizedMultilayerPerceptron(BaseMultilayerPerceptron):
"""
Customized MLP Perceptron based on
`BaseMultilayerPerceptron
<https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/neural_network/multilayer_perceptron.py#L40>`_.
"""
def __init__(self, hidden_layer_sizes, activation, solver,
alpha, batch_size, learning_rate, learning_rate_init, power_t,
max_iter, loss, shuffle, random_state, tol, verbose,
warm_start, momentum, nesterovs_momentum, early_stopping,
validation_fraction, beta_1, beta_2, epsilon,
n_iter_no_change):
BaseMultilayerPerceptron.__init__(self, hidden_layer_sizes, activation, solver,
alpha, batch_size, learning_rate, learning_rate_init, power_t,
max_iter, loss, shuffle, random_state, tol, verbose,
warm_start, momentum, nesterovs_momentum, early_stopping,
validation_fraction, beta_1, beta_2, epsilon,
n_iter_no_change)
def _get_loss_function(self, loss_func_name):
"""
Returns the loss functions.
@param loss_func_name loss function name, see
:epkg:`sklearn:neural_networks:MLPRegressor`
"""
return LOSS_FUNCTIONS.get(loss_func_name, EXTENDED_LOSS_FUNCTIONS[loss_func_name])
def _modify_loss_derivatives(self, last_deltas):
"""
Modifies the loss derivatives.
@param last_deltas last deltas is the difference between the output and the expected output
@return modified derivatives
"""
if self.loss == 'absolute_loss':
return DERIVATIVE_LOSS_FUNCTIONS['absolute_loss'](last_deltas)
else:
return last_deltas
def _backprop(self, X, y, activations, deltas, coef_grads,
intercept_grads):
"""
Computes the MLP loss function and its corresponding derivatives
with respect to each parameter: weights and bias vectors.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
y : array-like, shape (n_samples,)
The target values.
activations : list, length = n_layers - 1
The ith element of the list holds the values of the ith layer.
deltas : list, length = n_layers - 1
The ith element of the list holds the difference between the
activations of the i + 1 layer and the backpropagated error.
More specifically, deltas are gradients of loss with respect to z
in each layer, where z = wx + b is the value of a particular layer
before passing through the activation function
coef_grads : list, length = n_layers - 1
The ith element contains the amount of change used to update the
coefficient parameters of the ith layer in an iteration.
intercept_grads : list, length = n_layers - 1
The ith element contains the amount of change used to update the
intercept parameters of the ith layer in an iteration.
Returns
-------
loss : float
coef_grads : list, length = n_layers - 1
intercept_grads : list, length = n_layers - 1
"""
n_samples = X.shape[0]
# Forward propagate
activations = self._forward_pass(activations)
# Get loss
loss_func_name = self.loss
if loss_func_name == 'log_loss' and self.out_activation_ == 'logistic':
loss_func_name = 'binary_log_loss'
loss_function = self._get_loss_function(loss_func_name)
loss = loss_function(y, activations[-1])
# Add L2 regularization term to loss
values = np.sum(
np.array([np.dot(s.ravel(), s.ravel()) for s in self.coefs_]))
loss += (0.5 * self.alpha) * values / n_samples
# Backward propagate
last = self.n_layers_ - 2
# The calculation of delta[last] here works with following
# combinations of output activation and loss function:
# sigmoid and binary cross entropy, softmax and categorical cross
# entropy, and identity with squared loss
deltas[last] = activations[-1] - y
# We insert the following modification to modify the gradient
# due to the modification of the loss function.
deltas[last] = self._modify_loss_derivatives(deltas[last])
# Compute gradient for the last layer
coef_grads, intercept_grads = self._compute_loss_grad(
last, n_samples, activations, deltas, coef_grads, intercept_grads)
# Iterate over the hidden layers
for i in range(self.n_layers_ - 2, 0, -1):
deltas[i - 1] = safe_sparse_dot(deltas[i], self.coefs_[i].T)
inplace_derivative = DERIVATIVES[self.activation]
inplace_derivative(activations[i], deltas[i - 1])
coef_grads, intercept_grads = self._compute_loss_grad(
i - 1, n_samples, activations, deltas, coef_grads,
intercept_grads)
return loss, coef_grads, intercept_grads
class QuantileMLPRegressor(CustomizedMultilayerPerceptron, RegressorMixin):
"""
Quantile MLP Regression or neural networks regression
trained with norm :epkg:`L1`. This class inherits from
:epkg:`sklearn:neural_networks:MLPRegressor`.
This model optimizes the absolute-loss using LBFGS or stochastic gradient
descent. See @see cl CustomizedMultilayerPerceptron and
@see fn absolute_loss.
Parameters
----------
hidden_layer_sizes : tuple, length = n_layers - 2, default (100,)
The ith element represents the number of neurons in the ith
hidden layer.
activation : {'identity', 'logistic', 'tanh', 'relu'}, default 'relu'
Activation function for the hidden layer.
- 'identity', no-op activation, useful to implement linear bottleneck,
returns :math:`f(x) = x`
- 'logistic', the logistic sigmoid function,
returns :math:`f(x) = 1 / (1 + exp(-x))`.
- 'tanh', the hyperbolic tan function,
returns :math:`f(x) = tanh(x)`.
- 'relu', the rectified linear unit function,
returns :math:`f(x) = \\max(0, x)`.
solver : ``{'lbfgs', 'sgd', 'adam'}``, default 'adam'
The solver for weight optimization.
- *'lbfgs'* is an optimizer in the family of quasi-Newton methods.
- *'sgd'* refers to stochastic gradient descent.
- *'adam'* refers to a stochastic gradient-based optimizer proposed by
Kingma, Diederik, and Jimmy Ba
Note: The default solver 'adam' works pretty well on relatively
large datasets (with thousands of training samples or more) in terms of
both training time and validation score.
For small datasets, however, 'lbfgs' can converge faster and perform
better.
alpha : float, optional, default 0.0001
:epkg:`L2` penalty (regularization term) parameter.
batch_size : int, optional, default 'auto'
Size of minibatches for stochastic optimizers.
If the solver is 'lbfgs', the classifier will not use minibatch.
When set to "auto", `batch_size=min(200, n_samples)`
learning_rate : {'constant', 'invscaling', 'adaptive'}, default 'constant'
Learning rate schedule for weight updates.
- 'constant' is a constant learning rate given by
'learning_rate_init'.
- 'invscaling' gradually decreases the learning rate ``learning_rate_``
at each time step 't' using an inverse scaling exponent of 'power_t'.
effective_learning_rate = learning_rate_init / pow(t, power_t)
- 'adaptive' keeps the learning rate constant to
'learning_rate_init' as long as training loss keeps decreasing.
Each time two consecutive epochs fail to decrease training loss by at
least tol, or fail to increase validation score by at least tol if
'early_stopping' is on, the current learning rate is divided by 5.
Only used when solver='sgd'.
learning_rate_init : double, optional, default 0.001
The initial learning rate used. It controls the step-size
in updating the weights. Only used when solver='sgd' or 'adam'.
power_t : double, optional, default 0.5
The exponent for inverse scaling learning rate.
It is used in updating effective learning rate when the learning_rate
is set to 'invscaling'. Only used when solver='sgd'.
max_iter : int, optional, default 200
Maximum number of iterations. The solver iterates until convergence
(determined by 'tol') or this number of iterations. For stochastic
solvers ('sgd', 'adam'), note that this determines the number of epochs
(how many times each data point will be used), not the number of
gradient steps.
shuffle : bool, optional, default True
Whether to shuffle samples in each iteration. Only used when
solver='sgd' or 'adam'.
random_state : int, RandomState instance or None, optional, default None
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
tol : float, optional, default 1e-4
Tolerance for the optimization. When the loss or score is not improving
by at least ``tol`` for ``n_iter_no_change`` consecutive iterations,
unless ``learning_rate`` is set to 'adaptive', convergence is
considered to be reached and training stops.
verbose : bool, optional, default False
Whether to print progress messages to stdout.
warm_start : bool, optional, default False
When set to True, reuse the solution of the previous
call to fit as initialization, otherwise, just erase the
previous solution. See :term:`the Glossary <warm_start>`.
momentum : float, default 0.9
Momentum for gradient descent update. Should be between 0 and 1. Only
used when solver='sgd'.
nesterovs_momentum : boolean, default True
Whether to use Nesterov's momentum. Only used when solver='sgd' and
momentum > 0.
early_stopping : bool, default False
Whether to use early stopping to terminate training when validation
score is not improving. If set to true, it will automatically set
aside 10% of training data as validation and terminate training when
validation score is not improving by at least ``tol`` for
``n_iter_no_change`` consecutive epochs.
Only effective when solver='sgd' or 'adam'
validation_fraction : float, optional, default 0.1
The proportion of training data to set aside as validation set for
early stopping. Must be between 0 and 1.
Only used if early_stopping is True
beta_1 : float, optional, default 0.9
Exponential decay rate for estimates of first moment vector in adam,
should be in [0, 1). Only used when solver='adam'
beta_2 : float, optional, default 0.999
Exponential decay rate for estimates of second moment vector in adam,
should be in [0, 1). Only used when solver='adam'
epsilon : float, optional, default 1e-8
Value for numerical stability in adam. Only used when solver='adam'
n_iter_no_change : int, optional, default 10
Maximum number of epochs to not meet ``tol`` improvement.
Only effective when solver='sgd' or 'adam'
.. versionadded:: 0.20
Attributes
----------
loss_ : float
The current loss computed with the loss function.
coefs_ : list, length n_layers - 1
The ith element in the list represents the weight matrix corresponding
to layer i.
intercepts_ : list, length n_layers - 1
The ith element in the list represents the bias vector corresponding to
layer i + 1.
n_iter_ : int,
The number of iterations the solver has ran.
n_layers_ : int
Number of layers.
n_outputs_ : int
Number of outputs.
out_activation_ : string
Name of the output activation function.
Notes
-----
*QuantileMLPRegressor* trains iteratively since at each time step
the partial derivatives of the loss function with respect to the model
parameters are computed to update the parameters.
It can also have a regularization term added to the loss function
that shrinks model parameters to prevent overfitting.
This implementation works with data represented as dense and sparse numpy
arrays of floating point values.
References
----------
Hinton, Geoffrey E.
"Connectionist learning procedures." Artificial intelligence 40.1
(1989): 185-234.
Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of
training deep feedforward neural networks." International Conference
on Artificial Intelligence and Statistics. 2010.
He, Kaiming, et al. "Delving deep into rectifiers: Surpassing human-level
performance on imagenet classification." arXiv preprint
arXiv:1502.01852 (2015).
Kingma, Diederik, and Jimmy Ba. "Adam: A method for stochastic
optimization." arXiv preprint arXiv:1412.6980 (2014).
"""
def __init__(self,
hidden_layer_sizes=(100,), activation="relu",
solver='adam', alpha=0.0001,
batch_size='auto', learning_rate="constant",
learning_rate_init=0.001,
power_t=0.5, max_iter=200, shuffle=True,
random_state=None, tol=1e-4,
verbose=False, warm_start=False, momentum=0.9,
nesterovs_momentum=True, early_stopping=False,
validation_fraction=0.1, beta_1=0.9, beta_2=0.999,
epsilon=1e-8, n_iter_no_change=10):
"""
Parameters
----------
See :epkg:`sklearn:neural_networks:MLPRegressor`
"""
sup = super(QuantileMLPRegressor, self)
sup.__init__(hidden_layer_sizes=hidden_layer_sizes,
activation=activation, solver=solver, alpha=alpha,
batch_size=batch_size, learning_rate=learning_rate,
learning_rate_init=learning_rate_init, power_t=power_t,
max_iter=max_iter, loss='absolute_loss', shuffle=shuffle,
random_state=random_state, tol=tol, verbose=verbose,
warm_start=warm_start, momentum=momentum,
nesterovs_momentum=nesterovs_momentum,
early_stopping=early_stopping,
validation_fraction=validation_fraction,
beta_1=beta_1, beta_2=beta_2, epsilon=epsilon,
n_iter_no_change=n_iter_no_change)
def predict(self, X):
"""
Predicts using the multi-layer perceptron model.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
y : array-like, shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self, "coefs_")
y_pred = self._predict(X)
if y_pred.shape[1] == 1:
return y_pred.ravel()
return y_pred
def _validate_input(self, X, y, incremental):
X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'],
multi_output=True, y_numeric=True)
if y.ndim == 2 and y.shape[1] == 1:
y = column_or_1d(y, warn=True)
return X, y
def score(self, X, y, sample_weight=None):
"""
Returns mean absolute error regression loss.
Parameters
----------
X : array-like, shape = (n_samples, n_features)
Test samples.
y : array-like, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : array-like, shape = [n_samples], optional
Sample weights.
Returns
-------
score : float
mean absolute error regression loss
"""
pred = self.predict(X)
return mean_absolute_error(y, pred, sample_weight=sample_weight)
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