/
_multilayer_perceptron.py
1645 lines (1361 loc) · 59.1 KB
/
_multilayer_perceptron.py
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"""Multi-layer Perceptron
"""
# Authors: Issam H. Laradji <issam.laradji@gmail.com>
# Andreas Mueller
# Jiyuan Qian
# License: BSD 3 clause
import warnings
from abc import ABCMeta, abstractmethod
from itertools import chain
from numbers import Integral, Real
import numpy as np
import scipy.optimize
from ..base import (
BaseEstimator,
ClassifierMixin,
RegressorMixin,
_fit_context,
is_classifier,
)
from ..exceptions import ConvergenceWarning
from ..metrics import accuracy_score, r2_score
from ..model_selection import train_test_split
from ..preprocessing import LabelBinarizer
from ..utils import (
_safe_indexing,
check_random_state,
column_or_1d,
gen_batches,
shuffle,
)
from ..utils._param_validation import Interval, Options, StrOptions
from ..utils.extmath import safe_sparse_dot
from ..utils.metaestimators import available_if
from ..utils.multiclass import (
_check_partial_fit_first_call,
type_of_target,
unique_labels,
)
from ..utils.optimize import _check_optimize_result
from ..utils.validation import check_is_fitted
from ._base import ACTIVATIONS, DERIVATIVES, LOSS_FUNCTIONS
from ._stochastic_optimizers import AdamOptimizer, SGDOptimizer
_STOCHASTIC_SOLVERS = ["sgd", "adam"]
def _pack(coefs_, intercepts_):
"""Pack the parameters into a single vector."""
return np.hstack([l.ravel() for l in coefs_ + intercepts_])
class BaseMultilayerPerceptron(BaseEstimator, metaclass=ABCMeta):
"""Base class for MLP classification and regression.
Warning: This class should not be used directly.
Use derived classes instead.
.. versionadded:: 0.18
"""
_parameter_constraints: dict = {
"hidden_layer_sizes": [
"array-like",
Interval(Integral, 1, None, closed="left"),
],
"activation": [StrOptions({"identity", "logistic", "tanh", "relu"})],
"solver": [StrOptions({"lbfgs", "sgd", "adam"})],
"alpha": [Interval(Real, 0, None, closed="left")],
"batch_size": [
StrOptions({"auto"}),
Interval(Integral, 1, None, closed="left"),
],
"learning_rate": [StrOptions({"constant", "invscaling", "adaptive"})],
"learning_rate_init": [Interval(Real, 0, None, closed="neither")],
"power_t": [Interval(Real, 0, None, closed="left")],
"max_iter": [Interval(Integral, 1, None, closed="left")],
"shuffle": ["boolean"],
"random_state": ["random_state"],
"tol": [Interval(Real, 0, None, closed="left")],
"verbose": ["verbose"],
"warm_start": ["boolean"],
"momentum": [Interval(Real, 0, 1, closed="both")],
"nesterovs_momentum": ["boolean"],
"early_stopping": ["boolean"],
"validation_fraction": [Interval(Real, 0, 1, closed="left")],
"beta_1": [Interval(Real, 0, 1, closed="left")],
"beta_2": [Interval(Real, 0, 1, closed="left")],
"epsilon": [Interval(Real, 0, None, closed="neither")],
"n_iter_no_change": [
Interval(Integral, 1, None, closed="left"),
Options(Real, {np.inf}),
],
"max_fun": [Interval(Integral, 1, None, closed="left")],
}
@abstractmethod
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,
max_fun,
):
self.activation = activation
self.solver = solver
self.alpha = alpha
self.batch_size = batch_size
self.learning_rate = learning_rate
self.learning_rate_init = learning_rate_init
self.power_t = power_t
self.max_iter = max_iter
self.loss = loss
self.hidden_layer_sizes = hidden_layer_sizes
self.shuffle = shuffle
self.random_state = random_state
self.tol = tol
self.verbose = verbose
self.warm_start = warm_start
self.momentum = momentum
self.nesterovs_momentum = nesterovs_momentum
self.early_stopping = early_stopping
self.validation_fraction = validation_fraction
self.beta_1 = beta_1
self.beta_2 = beta_2
self.epsilon = epsilon
self.n_iter_no_change = n_iter_no_change
self.max_fun = max_fun
def _unpack(self, packed_parameters):
"""Extract the coefficients and intercepts from packed_parameters."""
for i in range(self.n_layers_ - 1):
start, end, shape = self._coef_indptr[i]
self.coefs_[i] = np.reshape(packed_parameters[start:end], shape)
start, end = self._intercept_indptr[i]
self.intercepts_[i] = packed_parameters[start:end]
def _forward_pass(self, activations):
"""Perform a forward pass on the network by computing the values
of the neurons in the hidden layers and the output layer.
Parameters
----------
activations : list, length = n_layers - 1
The ith element of the list holds the values of the ith layer.
"""
hidden_activation = ACTIVATIONS[self.activation]
# Iterate over the hidden layers
for i in range(self.n_layers_ - 1):
activations[i + 1] = safe_sparse_dot(activations[i], self.coefs_[i])
activations[i + 1] += self.intercepts_[i]
# For the hidden layers
if (i + 1) != (self.n_layers_ - 1):
hidden_activation(activations[i + 1])
# For the last layer
output_activation = ACTIVATIONS[self.out_activation_]
output_activation(activations[i + 1])
return activations
def _forward_pass_fast(self, X, check_input=True):
"""Predict using the trained model
This is the same as _forward_pass but does not record the activations
of all layers and only returns the last layer's activation.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
check_input : bool, default=True
Perform input data validation or not.
Returns
-------
y_pred : ndarray of shape (n_samples,) or (n_samples, n_outputs)
The decision function of the samples for each class in the model.
"""
if check_input:
X = self._validate_data(X, accept_sparse=["csr", "csc"], reset=False)
# Initialize first layer
activation = X
# Forward propagate
hidden_activation = ACTIVATIONS[self.activation]
for i in range(self.n_layers_ - 1):
activation = safe_sparse_dot(activation, self.coefs_[i])
activation += self.intercepts_[i]
if i != self.n_layers_ - 2:
hidden_activation(activation)
output_activation = ACTIVATIONS[self.out_activation_]
output_activation(activation)
return activation
def _compute_loss_grad(
self, layer, n_samples, activations, deltas, coef_grads, intercept_grads
):
"""Compute the gradient of loss with respect to coefs and intercept for
specified layer.
This function does backpropagation for the specified one layer.
"""
coef_grads[layer] = safe_sparse_dot(activations[layer].T, deltas[layer])
coef_grads[layer] += self.alpha * self.coefs_[layer]
coef_grads[layer] /= n_samples
intercept_grads[layer] = np.mean(deltas[layer], 0)
def _loss_grad_lbfgs(
self, packed_coef_inter, X, y, activations, deltas, coef_grads, intercept_grads
):
"""Compute the MLP loss function and its corresponding derivatives
with respect to the different parameters given in the initialization.
Returned gradients are packed in a single vector so it can be used
in lbfgs
Parameters
----------
packed_coef_inter : ndarray
A vector comprising the flattened coefficients and intercepts.
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
y : ndarray of 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
grad : array-like, shape (number of nodes of all layers,)
"""
self._unpack(packed_coef_inter)
loss, coef_grads, intercept_grads = self._backprop(
X, y, activations, deltas, coef_grads, intercept_grads
)
grad = _pack(coef_grads, intercept_grads)
return loss, grad
def _backprop(self, X, y, activations, deltas, coef_grads, intercept_grads):
"""Compute the MLP loss function and its corresponding derivatives
with respect to each parameter: weights and bias vectors.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
y : ndarray of 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 = LOSS_FUNCTIONS[loss_func_name](y, activations[-1])
# Add L2 regularization term to loss
values = 0
for s in self.coefs_:
s = s.ravel()
values += np.dot(s, s)
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
# Compute gradient for the last layer
self._compute_loss_grad(
last, n_samples, activations, deltas, coef_grads, intercept_grads
)
inplace_derivative = DERIVATIVES[self.activation]
# 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(activations[i], deltas[i - 1])
self._compute_loss_grad(
i - 1, n_samples, activations, deltas, coef_grads, intercept_grads
)
return loss, coef_grads, intercept_grads
def _initialize(self, y, layer_units, dtype):
# set all attributes, allocate weights etc. for first call
# Initialize parameters
self.n_iter_ = 0
self.t_ = 0
self.n_outputs_ = y.shape[1]
# Compute the number of layers
self.n_layers_ = len(layer_units)
# Output for regression
if not is_classifier(self):
self.out_activation_ = "identity"
# Output for multi class
elif self._label_binarizer.y_type_ == "multiclass":
self.out_activation_ = "softmax"
# Output for binary class and multi-label
else:
self.out_activation_ = "logistic"
# Initialize coefficient and intercept layers
self.coefs_ = []
self.intercepts_ = []
for i in range(self.n_layers_ - 1):
coef_init, intercept_init = self._init_coef(
layer_units[i], layer_units[i + 1], dtype
)
self.coefs_.append(coef_init)
self.intercepts_.append(intercept_init)
if self.solver in _STOCHASTIC_SOLVERS:
self.loss_curve_ = []
self._no_improvement_count = 0
if self.early_stopping:
self.validation_scores_ = []
self.best_validation_score_ = -np.inf
self.best_loss_ = None
else:
self.best_loss_ = np.inf
self.validation_scores_ = None
self.best_validation_score_ = None
def _init_coef(self, fan_in, fan_out, dtype):
# Use the initialization method recommended by
# Glorot et al.
factor = 6.0
if self.activation == "logistic":
factor = 2.0
init_bound = np.sqrt(factor / (fan_in + fan_out))
# Generate weights and bias:
coef_init = self._random_state.uniform(
-init_bound, init_bound, (fan_in, fan_out)
)
intercept_init = self._random_state.uniform(-init_bound, init_bound, fan_out)
coef_init = coef_init.astype(dtype, copy=False)
intercept_init = intercept_init.astype(dtype, copy=False)
return coef_init, intercept_init
def _fit(self, X, y, incremental=False):
# Make sure self.hidden_layer_sizes is a list
hidden_layer_sizes = self.hidden_layer_sizes
if not hasattr(hidden_layer_sizes, "__iter__"):
hidden_layer_sizes = [hidden_layer_sizes]
hidden_layer_sizes = list(hidden_layer_sizes)
if np.any(np.array(hidden_layer_sizes) <= 0):
raise ValueError(
"hidden_layer_sizes must be > 0, got %s." % hidden_layer_sizes
)
first_pass = not hasattr(self, "coefs_") or (
not self.warm_start and not incremental
)
X, y = self._validate_input(X, y, incremental, reset=first_pass)
n_samples, n_features = X.shape
# Ensure y is 2D
if y.ndim == 1:
y = y.reshape((-1, 1))
self.n_outputs_ = y.shape[1]
layer_units = [n_features] + hidden_layer_sizes + [self.n_outputs_]
# check random state
self._random_state = check_random_state(self.random_state)
if first_pass:
# First time training the model
self._initialize(y, layer_units, X.dtype)
# Initialize lists
activations = [X] + [None] * (len(layer_units) - 1)
deltas = [None] * (len(activations) - 1)
coef_grads = [
np.empty((n_fan_in_, n_fan_out_), dtype=X.dtype)
for n_fan_in_, n_fan_out_ in zip(layer_units[:-1], layer_units[1:])
]
intercept_grads = [
np.empty(n_fan_out_, dtype=X.dtype) for n_fan_out_ in layer_units[1:]
]
# Run the Stochastic optimization solver
if self.solver in _STOCHASTIC_SOLVERS:
self._fit_stochastic(
X,
y,
activations,
deltas,
coef_grads,
intercept_grads,
layer_units,
incremental,
)
# Run the LBFGS solver
elif self.solver == "lbfgs":
self._fit_lbfgs(
X, y, activations, deltas, coef_grads, intercept_grads, layer_units
)
# validate parameter weights
weights = chain(self.coefs_, self.intercepts_)
if not all(np.isfinite(w).all() for w in weights):
raise ValueError(
"Solver produced non-finite parameter weights. The input data may"
" contain large values and need to be preprocessed."
)
return self
def _fit_lbfgs(
self, X, y, activations, deltas, coef_grads, intercept_grads, layer_units
):
# Store meta information for the parameters
self._coef_indptr = []
self._intercept_indptr = []
start = 0
# Save sizes and indices of coefficients for faster unpacking
for i in range(self.n_layers_ - 1):
n_fan_in, n_fan_out = layer_units[i], layer_units[i + 1]
end = start + (n_fan_in * n_fan_out)
self._coef_indptr.append((start, end, (n_fan_in, n_fan_out)))
start = end
# Save sizes and indices of intercepts for faster unpacking
for i in range(self.n_layers_ - 1):
end = start + layer_units[i + 1]
self._intercept_indptr.append((start, end))
start = end
# Run LBFGS
packed_coef_inter = _pack(self.coefs_, self.intercepts_)
if self.verbose is True or self.verbose >= 1:
iprint = 1
else:
iprint = -1
opt_res = scipy.optimize.minimize(
self._loss_grad_lbfgs,
packed_coef_inter,
method="L-BFGS-B",
jac=True,
options={
"maxfun": self.max_fun,
"maxiter": self.max_iter,
"iprint": iprint,
"gtol": self.tol,
},
args=(X, y, activations, deltas, coef_grads, intercept_grads),
)
self.n_iter_ = _check_optimize_result("lbfgs", opt_res, self.max_iter)
self.loss_ = opt_res.fun
self._unpack(opt_res.x)
def _fit_stochastic(
self,
X,
y,
activations,
deltas,
coef_grads,
intercept_grads,
layer_units,
incremental,
):
params = self.coefs_ + self.intercepts_
if not incremental or not hasattr(self, "_optimizer"):
if self.solver == "sgd":
self._optimizer = SGDOptimizer(
params,
self.learning_rate_init,
self.learning_rate,
self.momentum,
self.nesterovs_momentum,
self.power_t,
)
elif self.solver == "adam":
self._optimizer = AdamOptimizer(
params,
self.learning_rate_init,
self.beta_1,
self.beta_2,
self.epsilon,
)
# early_stopping in partial_fit doesn't make sense
if self.early_stopping and incremental:
raise ValueError("partial_fit does not support early_stopping=True")
early_stopping = self.early_stopping
if early_stopping:
# don't stratify in multilabel classification
should_stratify = is_classifier(self) and self.n_outputs_ == 1
stratify = y if should_stratify else None
X, X_val, y, y_val = train_test_split(
X,
y,
random_state=self._random_state,
test_size=self.validation_fraction,
stratify=stratify,
)
if is_classifier(self):
y_val = self._label_binarizer.inverse_transform(y_val)
else:
X_val = None
y_val = None
n_samples = X.shape[0]
sample_idx = np.arange(n_samples, dtype=int)
if self.batch_size == "auto":
batch_size = min(200, n_samples)
else:
if self.batch_size > n_samples:
warnings.warn(
"Got `batch_size` less than 1 or larger than "
"sample size. It is going to be clipped"
)
batch_size = np.clip(self.batch_size, 1, n_samples)
try:
self.n_iter_ = 0
for it in range(self.max_iter):
if self.shuffle:
# Only shuffle the sample indices instead of X and y to
# reduce the memory footprint. These indices will be used
# to slice the X and y.
sample_idx = shuffle(sample_idx, random_state=self._random_state)
accumulated_loss = 0.0
for batch_slice in gen_batches(n_samples, batch_size):
if self.shuffle:
X_batch = _safe_indexing(X, sample_idx[batch_slice])
y_batch = y[sample_idx[batch_slice]]
else:
X_batch = X[batch_slice]
y_batch = y[batch_slice]
activations[0] = X_batch
batch_loss, coef_grads, intercept_grads = self._backprop(
X_batch,
y_batch,
activations,
deltas,
coef_grads,
intercept_grads,
)
accumulated_loss += batch_loss * (
batch_slice.stop - batch_slice.start
)
# update weights
grads = coef_grads + intercept_grads
self._optimizer.update_params(params, grads)
self.n_iter_ += 1
self.loss_ = accumulated_loss / X.shape[0]
self.t_ += n_samples
self.loss_curve_.append(self.loss_)
if self.verbose:
print("Iteration %d, loss = %.8f" % (self.n_iter_, self.loss_))
# update no_improvement_count based on training loss or
# validation score according to early_stopping
self._update_no_improvement_count(early_stopping, X_val, y_val)
# for learning rate that needs to be updated at iteration end
self._optimizer.iteration_ends(self.t_)
if self._no_improvement_count > self.n_iter_no_change:
# not better than last `n_iter_no_change` iterations by tol
# stop or decrease learning rate
if early_stopping:
msg = (
"Validation score did not improve more than "
"tol=%f for %d consecutive epochs."
% (self.tol, self.n_iter_no_change)
)
else:
msg = (
"Training loss did not improve more than tol=%f"
" for %d consecutive epochs."
% (self.tol, self.n_iter_no_change)
)
is_stopping = self._optimizer.trigger_stopping(msg, self.verbose)
if is_stopping:
break
else:
self._no_improvement_count = 0
if incremental:
break
if self.n_iter_ == self.max_iter:
warnings.warn(
"Stochastic Optimizer: Maximum iterations (%d) "
"reached and the optimization hasn't converged yet."
% self.max_iter,
ConvergenceWarning,
)
except KeyboardInterrupt:
warnings.warn("Training interrupted by user.")
if early_stopping:
# restore best weights
self.coefs_ = self._best_coefs
self.intercepts_ = self._best_intercepts
def _update_no_improvement_count(self, early_stopping, X_val, y_val):
if early_stopping:
# compute validation score, use that for stopping
self.validation_scores_.append(self._score(X_val, y_val))
if self.verbose:
print("Validation score: %f" % self.validation_scores_[-1])
# update best parameters
# use validation_scores_, not loss_curve_
# let's hope no-one overloads .score with mse
last_valid_score = self.validation_scores_[-1]
if last_valid_score < (self.best_validation_score_ + self.tol):
self._no_improvement_count += 1
else:
self._no_improvement_count = 0
if last_valid_score > self.best_validation_score_:
self.best_validation_score_ = last_valid_score
self._best_coefs = [c.copy() for c in self.coefs_]
self._best_intercepts = [i.copy() for i in self.intercepts_]
else:
if self.loss_curve_[-1] > self.best_loss_ - self.tol:
self._no_improvement_count += 1
else:
self._no_improvement_count = 0
if self.loss_curve_[-1] < self.best_loss_:
self.best_loss_ = self.loss_curve_[-1]
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y):
"""Fit the model to data matrix X and target(s) y.
Parameters
----------
X : ndarray or sparse matrix of shape (n_samples, n_features)
The input data.
y : ndarray of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels in classification, real numbers in
regression).
Returns
-------
self : object
Returns a trained MLP model.
"""
return self._fit(X, y, incremental=False)
def _check_solver(self):
if self.solver not in _STOCHASTIC_SOLVERS:
raise AttributeError(
"partial_fit is only available for stochastic"
" optimizers. %s is not stochastic."
% self.solver
)
return True
class MLPClassifier(ClassifierMixin, BaseMultilayerPerceptron):
"""Multi-layer Perceptron classifier.
This model optimizes the log-loss function using LBFGS or stochastic
gradient descent.
.. versionadded:: 0.18
Parameters
----------
hidden_layer_sizes : array-like of shape(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 f(x) = x
- 'logistic', the logistic sigmoid function,
returns f(x) = 1 / (1 + exp(-x)).
- 'tanh', the hyperbolic tan function,
returns f(x) = tanh(x).
- 'relu', the rectified linear unit function,
returns 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, default=0.0001
Strength of the L2 regularization term. The L2 regularization term
is divided by the sample size when added to the loss.
batch_size : int, 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 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 : float, 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 : float, 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, 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, default=True
Whether to shuffle samples in each iteration. Only used when
solver='sgd' or 'adam'.
random_state : int, RandomState instance, default=None
Determines random number generation for weights and bias
initialization, train-test split if early stopping is used, and batch
sampling when solver='sgd' or 'adam'.
Pass an int for reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
tol : float, 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, default=False
Whether to print progress messages to stdout.
warm_start : bool, 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 : bool, 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. The split is stratified,
except in a multilabel setting.
If early stopping is False, then the training stops when the training
loss does not improve by more than tol for n_iter_no_change consecutive
passes over the training set.
Only effective when solver='sgd' or 'adam'.
validation_fraction : float, 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, 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, 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, default=1e-8
Value for numerical stability in adam. Only used when solver='adam'.
n_iter_no_change : int, default=10
Maximum number of epochs to not meet ``tol`` improvement.
Only effective when solver='sgd' or 'adam'.
.. versionadded:: 0.20
max_fun : int, default=15000
Only used when solver='lbfgs'. Maximum number of loss function calls.
The solver iterates until convergence (determined by 'tol'), number
of iterations reaches max_iter, or this number of loss function calls.
Note that number of loss function calls will be greater than or equal
to the number of iterations for the `MLPClassifier`.
.. versionadded:: 0.22
Attributes
----------
classes_ : ndarray or list of ndarray of shape (n_classes,)
Class labels for each output.
loss_ : float
The current loss computed with the loss function.
best_loss_ : float or None
The minimum loss reached by the solver throughout fitting.
If `early_stopping=True`, this attribute is set to `None`. Refer to
the `best_validation_score_` fitted attribute instead.
loss_curve_ : list of shape (`n_iter_`,)
The ith element in the list represents the loss at the ith iteration.
validation_scores_ : list of shape (`n_iter_`,) or None
The score at each iteration on a held-out validation set. The score
reported is the accuracy score. Only available if `early_stopping=True`,
otherwise the attribute is set to `None`.
best_validation_score_ : float or None
The best validation score (i.e. accuracy score) that triggered the
early stopping. Only available if `early_stopping=True`, otherwise the
attribute is set to `None`.
t_ : int
The number of training samples seen by the solver during fitting.
coefs_ : list of shape (n_layers - 1,)
The ith element in the list represents the weight matrix corresponding
to layer i.
intercepts_ : list of shape (n_layers - 1,)
The ith element in the list represents the bias vector corresponding to
layer i + 1.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_iter_ : int
The number of iterations the solver has run.
n_layers_ : int
Number of layers.
n_outputs_ : int
Number of outputs.
out_activation_ : str
Name of the output activation function.
See Also
--------
MLPRegressor : Multi-layer Perceptron regressor.
BernoulliRBM : Bernoulli Restricted Boltzmann Machine (RBM).
Notes
-----
MLPClassifier 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.