MLPRegressor #

classsklearn.neural_network.MLPRegressor(loss='squared_error',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=1e-08,n_iter_no_change=10,max_fun=15000)[source]#

Multi-layer Perceptron regressor.

This model optimizes the squared error using LBFGS or stochastic gradientdescent.

Added in version 0.18.

Parameters:

loss{‘squared_error’, ‘poisson’}, default=’squared_error’

The loss function to use when training the weights. Note that the“squared error” and “poisson” losses actually implement“half squares error” and “half poisson deviance” to simplify thecomputation of the gradient. Furthermore, the “poisson” loss internally usesa log-link (exponential as the output activation function) and requiresy>=0.

Changed in version 1.7:Added parameterloss and option ‘poisson’.

hidden_layer_sizesarray-like of shape(n_layers - 2,), default=(100,)

The ith element represents the number of neurons in the ithhidden 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 byKingma, Diederik, and Jimmy Ba

For a comparison between Adam optimizer and SGD, seeCompare Stochastic learning strategies for MLPClassifier.

Note: The default solver ‘adam’ works pretty well on relativelylarge datasets (with thousands of training samples or more) in terms ofboth training time and validation score.For small datasets, however, ‘lbfgs’ can converge faster and performbetter.

alphafloat, default=0.0001

Strength of the L2 regularization term. The L2 regularization termis divided by the sample size when added to the loss.

batch_sizeint, default=’auto’

Size of minibatches for stochastic optimizers.If the solver is ‘lbfgs’, the regressor 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 ratelearning_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 atleast 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_initfloat, default=0.001

The initial learning rate used. It controls the step-sizein updating the weights. Only used when solver=’sgd’ or ‘adam’.

power_tfloat, default=0.5

The exponent for inverse scaling learning rate.It is used in updating effective learning rate when the learning_rateis 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 stochasticsolvers (‘sgd’, ‘adam’), note that this determines the number of epochs(how many times each data point will be used), not the number ofgradient steps.

shufflebool, default=True

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

random_stateint, RandomState instance, default=None

Determines random number generation for weights and biasinitialization, train-test split if early stopping is used, and batchsampling when solver=’sgd’ or ‘adam’.Pass an int for reproducible results across multiple function calls.SeeGlossary.

tolfloat, default=1e-4

Tolerance for the optimization. When the loss or score is not improvingby at leasttol forn_iter_no_change consecutive iterations,unlesslearning_rate is set to ‘adaptive’, convergence isconsidered 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 previouscall to fit as initialization, otherwise, just erase theprevious solution. Seethe Glossary.

momentumfloat, default=0.9

Momentum for gradient descent update. Should be between 0 and 1. Onlyused when solver=’sgd’.

nesterovs_momentumbool, default=True

Whether to use Nesterov’s momentum. Only used when solver=’sgd’ andmomentum > 0.

early_stoppingbool, default=False

Whether to use early stopping to terminate training when validationscore is not improving. If set to True, it will automatically setasidevalidation_fraction of training data as validation andterminate training when validation score is not improving by atleasttol 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 forearly 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=1e-8

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

n_iter_no_changeint, default=10

Maximum number of epochs to not meettol improvement.Only effective when solver=’sgd’ or ‘adam’.

Added in version 0.20.

max_funint, default=15000

Only used when solver=’lbfgs’. Maximum number of function calls.The solver iterates until convergence (determined bytol), numberof iterations reaches max_iter, or this number of function calls.Note that number of function calls will be greater than or equal tothe number of iterations for the MLPRegressor.

Added 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.Ifearly_stopping=True, this attribute is set toNone. Refer tothebest_validation_score_ fitted attribute instead.Only accessible when solver=’sgd’ or ‘adam’.
loss_curve_list of shape (n_iter_,): Loss value evaluated at the end of each training step.The ith element in the list represents the loss at the ith iteration.Only accessible when solver=’sgd’ or ‘adam’.
validation_scores_list of shape (n_iter_,) or None: The score at each iteration on a held-out validation set. The scorereported is the R2 score. Only available ifearly_stopping=True,otherwise the attribute is set toNone.Only accessible when solver=’sgd’ or ‘adam’.
best_validation_score_float or None: The best validation score (i.e. R2 score) that triggered theearly stopping. Only available ifearly_stopping=True, otherwise theattribute is set toNone.Only accessible when solver=’sgd’ or ‘adam’.
t_int: The number of training samples seen by the solver during fitting.Mathematically equalsn_iters*X.shape[0], it meanstime_step and it is used by optimizer’s learning rate scheduler.
coefs_list of shape (n_layers - 1,): The ith element in the list represents the weight matrix correspondingto layer i.
intercepts_list of shape (n_layers - 1,): The ith element in the list represents the bias vector corresponding tolayer i + 1.
n_features_in_int: Number of features seen duringfit.
Added in version 0.24.
feature_names_in_ndarray of shape (n_features_in_,): Names of features seen duringfit. Defined only whenXhas feature names that are all strings.
Added in version 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

BernoulliRBM: Bernoulli Restricted Boltzmann Machine (RBM).
MLPClassifier: Multi-layer Perceptron classifier.
sklearn.linear_model.SGDRegressor: Linear model fitted by minimizing a regularized empirical loss with SGD.

Notes

MLPRegressor trains iteratively since at each time stepthe partial derivatives of the loss function with respect to the modelparameters are computed to update the parameters.

It can also have a regularization term added to the loss functionthat shrinks model parameters to prevent overfitting.

This implementation works with data represented as dense and sparse numpyarrays 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 (2015). “Delving deep into rectifiers:Surpassing human-level performance on imagenet classification.”

Kingma, Diederik, and Jimmy Ba (2014)“Adam: A method for stochastic optimization.”

Examples

>>>fromsklearn.neural_networkimportMLPRegressor>>>fromsklearn.datasetsimportmake_regression>>>fromsklearn.model_selectionimporttrain_test_split>>>X,y=make_regression(n_samples=200,n_features=20,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=2000,tol=0.1)>>>regr.fit(X_train,y_train)MLPRegressor(max_iter=2000, random_state=1, tol=0.1)>>>regr.predict(X_test[:2])array([  28.98, -291])>>>regr.score(X_test,y_test)0.98

fit(X,y,sample_weight=None)[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 inregression).
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.
Added in version 1.7.

Returns:

selfobject: Returns a trained MLP model.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest: AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

partial_fit(X,y,sample_weight=None)[source]#

Update the model with a single iteration over the given data.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The input data.
yndarray of shape (n_samples,): The target values.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.
Added in version 1.6.

Returns:

selfobject: Trained MLP model.

predict(X)[source]#

Predict using the multi-layer perceptron model.

Parameters:

X{array-like, 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]#

Returncoefficient of determination on test data.

The coefficient of determination,$R^2$, is defined as$(1 - \frac{u}{v})$, where$u$ is the residualsum 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 themodel can be arbitrarily worse). A constant model that always predictsthe expected value ofy, disregarding the input features, would geta$R^2$ score of 0.0.

Parameters:

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputedkernel matrix or a list of generic objects instead with shape(n_samples,n_samples_fitted), wheren_samples_fittedis the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True values forX.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: $R^2$ ofself.predict(X) w.r.t.y.

Notes

The$R^2$ score used when callingscore on a regressor usesmultioutput='uniform_average' from version 0.23 to keep consistentwith default value ofr2_score.This influences thescore method of all the multioutputregressors (except forMultiOutputRegressor).

set_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→MLPRegressor[source]#

Configure whether metadata should be requested to be passed to thefit method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

True: metadata is requested, and passed tofit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it tofit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter infit.

Returns:

selfobject: The updated object.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects(such asPipeline). The latter haveparameters of the form<component>__<parameter> so that it’spossible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

set_partial_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→MLPRegressor[source]#

Configure whether metadata should be requested to be passed to thepartial_fit method.

The options for each parameter are:

True: metadata is requested, and passed topartial_fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it topartial_fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter inpartial_fit.

Returns:

selfobject: The updated object.

set_score_request(*,sample_weight:bool|None|str='$UNCHANGED$')→MLPRegressor[source]#

Configure whether metadata should be requested to be passed to thescore method.

The options for each parameter are:

True: metadata is requested, and passed toscore if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it toscore.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter inscore.

Returns:

selfobject: The updated object.

Gallery examples#

Time-related feature engineering

Partial Dependence and Individual Conditional Expectation Plots

Advanced Plotting With Partial Dependence

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Gallery examples#

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