sklearn.neural_network
.MLPClassifier¶

class
sklearn.neural_network.
MLPClassifier
(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 classifier.
This model optimizes the logloss function 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 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 for
n_iter_no_change
consecutive epochs. The split is stratified, except in a multilabel setting. 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 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
.New in version 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
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
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.
This implementation works with data represented as dense numpy arrays or sparse scipy 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 MLPClassifier >>> from sklearn.datasets import make_classification >>> from sklearn.model_selection import train_test_split >>> X, y = make_classification(n_samples=100, random_state=1) >>> X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, ... random_state=1) >>> clf = MLPClassifier(random_state=1, max_iter=300).fit(X_train, y_train) >>> clf.predict_proba(X_test[:1]) array([[0.038..., 0.961...]]) >>> clf.predict(X_test[:5, :]) array([1, 0, 1, 0, 1]) >>> clf.score(X_test, y_test) 0.8...
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 classifier
Return the log of probability estimates.
Probability estimates.
score
(X, y[, sample_weight])Return the mean accuracy on the given test data and labels.
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, 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
 paramsmapping of string to any
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}, shape (n_samples, n_features)
The input data.
 yarraylike, shape (n_samples,)
The target values.
 classesarray, shape (n_classes), default None
Classes across all calls to partial_fit. Can be obtained via
np.unique(y_all)
, where y_all is the target vector of the entire dataset. This argument is required for the first call to partial_fit and can be omitted in the subsequent calls. Note that y doesn’t need to contain all labels inclasses
.
 Returns
 selfreturns a trained MLP model.

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

predict_log_proba
(X)[source]¶ Return the log of probability estimates.
 Parameters
 Xndarray of shape (n_samples, n_features)
The input data.
 Returns
 log_y_probndarray of shape (n_samples, n_classes)
The predicted logprobability of the sample for each class in the model, where classes are ordered as they are in
self.classes_
. Equivalent to log(predict_proba(X))

predict_proba
(X)[source]¶ Probability estimates.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
The input data.
 Returns
 y_probndarray of shape (n_samples, n_classes)
The predicted probability of the sample for each class in the model, where classes are ordered as they are in
self.classes_
.

score
(X, y, sample_weight=None)[source]¶ Return the mean accuracy on the given test data and labels.
In multilabel classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Test samples.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True labels for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
Mean accuracy of self.predict(X) wrt. y.

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). 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
 selfobject
Estimator instance.