sklearn.neural_network.MLPRegressor

class sklearn.neural_network.MLPRegressor(hidden_layer_sizes=(100, ), activation='relu', algorithm='adam', alpha=0.0001, batch_size=200, learning_rate='constant', learning_rate_init=0.001, power_t=0.5, max_iter=200, shuffle=True, random_state=None, tol=0.0001, 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-08)

Multi-layer Perceptron regressor.

This algorithm optimizes the squared-loss using l-bfgs or gradient descent.

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 : {‘logistic’, ‘tanh’, ‘relu’}, default ‘relu’

Activation function for the hidden layer.

• ‘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)

algorithm : {‘l-bfgs’, ‘sgd’, ‘adam’}, default ‘adam’

The algorithm for weight optimization.

• ‘l-bfgs’ is an optimization algorithm in the family of quasi-Newton methods.
• ‘sgd’ refers to stochastic gradient descent.
• ‘adam’ refers to a stochastic gradient-based optimization algorithm proposed by Kingma, Diederik, and Jimmy Ba

Note: The default algorithm ‘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, ‘l-bfgs’ can converge faster and perform better.

alpha : float, optional, default 0.0001

L2 penalty (regularization term) parameter.

batch_size : int, optional, default 200

Size of minibatches for stochastic optimizers. If the algorithm is ‘l-bfgs’, the classifier will not use minibatch.

learning_rate : {‘constant’, ‘invscaling’, ‘adaptive’}, default ‘constant’

Learning rate schedule for weight updates.

-‘constant’, is a constant learnign 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 algorithm=’sgd’.

max_iter : int, optional, default 200

Maximum number of iterations. The algorithm iterates until convergence (determined by ‘tol’) or this number of iterations.

random_state : int or RandomState, optional, default None

State or seed for random number generator.

shuffle : bool, optional, default True

Whether to shuffle samples in each iteration. Only used when algorithm=’sgd’ or ‘adam’.

tol : float, optional, default 1e-4

Tolerance for the optimization. When the loss or score is not improving by at least tol for two consecutive iterations, unless learning_rate is set to ‘adaptive’, convergence is considered to be reached and training stops.

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 algorithm=’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 algorithm=’sgd’.

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.

momentum : float, default 0.9

Momentum for gradient descent update. Should be between 0 and 1. Only used when algorithm=’sgd’.

nesterovs_momentum : boolean, default True

Whether to use Nesterov’s momentum. Only used when algorithm=’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 two consecutive epochs. Only effective when algorithm=’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 algorithm=’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 algorithm=’adam’

epsilon : float, optional, default 1e-8

Value for numerical stability in adam. Only used when algorithm=’adam’

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 algorithm has ran.

n_layers_ : int

Number of layers.

`n_outputs_` : int

Number of outputs.

`out_activation_` : string

Name of the output activation function.

Notes

MLPRegressor 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).

Methods

fit(X, y)	Fit the model to data matrix X and target y.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict using the multi-layer perceptron model.
score(X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of this estimator.

__init__(hidden_layer_sizes=(100, ), activation='relu', algorithm='adam', alpha=0.0001, batch_size=200, learning_rate='constant', learning_rate_init=0.001, power_t=0.5, max_iter=200, shuffle=True, random_state=None, tol=0.0001, 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-08)

fit(X, y)

Fit the model to data matrix X and target y.

Parameters:

X : {array-like, sparse matrix}, shape (n_samples, n_features)

The input data.

y : array-like, shape (n_samples,)

The target values.

Returns:

self : returns a trained MLP model.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params : mapping of string to any

Parameter names mapped to their values.

partial_fit

Fit the model to data matrix X and target y.

Parameters:

X : {array-like, sparse matrix}, shape (n_samples, n_features)

The input data.

y : array-like, shape (n_samples,)

The target values.

Returns:

self : returns a trained MLP model.

predict(X)

Predict 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.

score(X, y, sample_weight=None)

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

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

R^2 of self.predict(X) wrt. y.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:self :