sklearn.neural_network
.MLPRegressor¶

class
sklearn.neural_network.
MLPRegressor
(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=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=1e08, n_iter_no_change=10, max_fun=15000)[source]¶ Multilayer Perceptron regressor.
This model optimizes the squaredloss using LBFGS or stochastic gradient descent.
New in version 0.18.
 Parameters
 hidden_layer_sizestuple, 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’, noop 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 quasiNewton methods.
‘sgd’ refers to stochastic gradient descent.
‘adam’ refers to a stochastic gradientbased 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.
 alphafloat, default=0.0001
L2 penalty (regularization term) parameter.
 batch_sizeint, 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_initdouble, default=0.001
The initial learning rate used. It controls the stepsize in updating the weights. Only used when solver=’sgd’ or ‘adam’.
 power_tdouble, 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_iterint, 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.
 shufflebool, default=True
Whether to shuffle samples in each iteration. Only used when solver=’sgd’ or ‘adam’.
 random_stateint, RandomState instance, default=None
Determines random number generation for weights and bias initialization, traintest 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 Glossary.
 tolfloat, default=1e4
Tolerance for the optimization. When the loss or score is not improving by at least
tol
forn_iter_no_change
consecutive iterations, unlesslearning_rate
is set to ‘adaptive’, convergence is considered to be reached and training stops. verbosebool, default=False
Whether to print progress messages to stdout.
 warm_startbool, default=False
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
 momentumfloat, default=0.9
Momentum for gradient descent update. Should be between 0 and 1. Only used when solver=’sgd’.
 nesterovs_momentumbool, default=True
Whether to use Nesterov’s momentum. Only used when solver=’sgd’ and momentum > 0.
 early_stoppingbool, 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
forn_iter_no_change
consecutive epochs. Only effective when solver=’sgd’ or ‘adam’ validation_fractionfloat, 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_1float, 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_2float, default=0.999
Exponential decay rate for estimates of second moment vector in adam, should be in [0, 1). Only used when solver=’adam’
 epsilonfloat, default=1e8
Value for numerical stability in adam. Only used when solver=’adam’
 n_iter_no_changeint, default=10
Maximum number of epochs to not meet
tol
improvement. Only effective when solver=’sgd’ or ‘adam’New in version 0.20.
 max_funint, default=15000
Only used when solver=’lbfgs’. Maximum number of function calls. The solver iterates until convergence (determined by ‘tol’), number of iterations reaches max_iter, or this number of function calls. Note that number of function calls will be greater than or equal to the number of iterations for the MLPRegressor.
New in version 0.22.
 Attributes
 loss_float
The current loss computed with the loss function.
 best_loss_float
The minimum loss reached by the solver throughout fitting.
 loss_curve_list of shape (
n_iter_
,) The ith element in the list represents the loss at the ith iteration.
 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_iter_int
The number of iterations the solver has ran.
 n_layers_int
Number of layers.
 n_outputs_int
Number of outputs.
 out_activation_str
Name of the output activation function.
 loss_curve_list of shape (n_iters,)
Loss value evaluated at the end of each training step.
 t_int
Mathematically equals
n_iters * X.shape[0]
, it meanstime_step
and it is used by optimizer’s learning rate scheduler.
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): 185234.
 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 humanlevel
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).
Examples
>>> from sklearn.neural_network import MLPRegressor >>> from sklearn.datasets import make_regression >>> from sklearn.model_selection import train_test_split >>> X, y = make_regression(n_samples=200, random_state=1) >>> X_train, X_test, y_train, y_test = train_test_split(X, y, ... random_state=1) >>> regr = MLPRegressor(random_state=1, max_iter=500).fit(X_train, y_train) >>> regr.predict(X_test[:2]) array([0.9..., 7.1...]) >>> regr.score(X_test, y_test) 0.4...
Methods
fit
(X, y)Fit the model to data matrix X and target(s) y.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict using the multilayer perceptron model.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.

fit
(X, y)[source]¶ Fit the model to data matrix X and target(s) y.
 Parameters
 Xndarray or sparse matrix of shape (n_samples, n_features)
The input data.
 yndarray of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels in classification, real numbers in regression).
 Returns
 selfreturns a trained MLP model.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsdict
Parameter names mapped to their values.

property
partial_fit
¶ Update the model with a single iteration over the given data.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
The input data.
 yndarray of shape (n_samples,)
The target values.
 Returns
 selfreturns a trained MLP model.

predict
(X)[source]¶ Predict using the multilayer perceptron model.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
The input data.
 Returns
 yndarray of shape (n_samples, n_outputs)
The predicted values.

score
(X, y, sample_weight=None)[source]¶ Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1  \frac{u}{v})\), where \(u\) is the residual sum of squares
((y_true  y_pred) ** 2).sum()
and \(v\) is the total sum of squares((y_true  y_true.mean()) ** 2).sum()
. The 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 ofy
, disregarding the input features, would get a \(R^2\) score of 0.0. Parameters
 Xarraylike of shape (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape
(n_samples, n_samples_fitted)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator. yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
. sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
\(R^2\) of
self.predict(X)
wrt.y
.
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfestimator instance
Estimator instance.