"""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

)

"""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

For a comparison between Adam optimizer and SGD, see

:ref:`sphx_glr_auto_examples_neural_networks_plot_mlp_training_curves.py`.

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.

For an example usage and visualization of varying regularization, see

:ref:`sphx_glr_auto_examples_neural_networks_plot_mlp_alpha.py`.

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.