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# `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=1e-08, n_iter_no_change=10, max_fun=15000)

  Multi-layer Perceptron classifier.

  This model optimizes the log-loss function using LBFGS or stochastic gradient descent.

  New in version 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

      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.

    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 Glossary.

    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 the Glossary.

    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’.

      New in version 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`.

      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 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 fit.

      New in version 0.24.

    feature_names_in_ndarray of shape (`n_features_in_`,)

      Names of features seen during fit. Defined only when `X` has feature names that are all strings.

      New 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

  `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.

  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): 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

      >>> 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_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `partial_fit`(X, y[, classes]) | Update the model with a single iteration over the given data.
  `predict`(X) | Predict using the multi-layer perceptron classifier.
  `predict_log_proba`(X) | Return the log of probability estimates.
  `predict_proba`(X) | 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.
  `set_partial_fit_request`(*[, classes]) | Request metadata passed to the `partial_fit` method.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.

  fit(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.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

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

    Returns:
      params dict

        Parameter names mapped to their values.

  partial_fit(X, y, classes=None)

    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.

      y array-like of shape (n_samples,)

        The target values.

      classes array of 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 in `classes`.

    Returns:
      self object

        Trained MLP model.

  predict(X)

    Predict using the multi-layer perceptron classifier.

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

        The input data.

    Returns:
      y ndarray, shape (n_samples,) or (n_samples, n_classes)

        The predicted classes.

  predict_log_proba(X)

    Return the log of probability estimates.

    Parameters:
      X ndarray of shape (n_samples, n_features)

        The input data.

    Returns:
      log_y_prob ndarray of shape (n_samples, n_classes)

        The predicted log-probability 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)

    Probability estimates.

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

        The input data.

    Returns:
      y_prob ndarray 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)

    Return the mean accuracy on the given test data and labels.

    In multi-label 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:
      X array-like of shape (n_samples, n_features)

        Test samples.

      y array-like of shape (n_samples,) or (n_samples, n_outputs)

        True labels for `X`.

      sample_weight array-like of shape (n_samples,), default=None

        Sample weights.

    Returns:
      score float

        Mean accuracy of `self.predict(X)` w.r.t. `y`.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  set_partial_fit_request(*, classes: bool | None | str = '$UNCHANGED$') → MLPClassifier

    Request metadata passed to the `partial_fit` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `partial_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 to `partial_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 the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      classes str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `classes` parameter in `partial_fit`.

    Returns:
      self object

        The updated object.

  set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → MLPClassifier

    Request metadata passed to the `score` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `score` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `score`.

    - `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 the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `score`.

    Returns:
      self object

        The updated object.

## Examples using `sklearn.neural_network.MLPClassifier`

Classifier comparison

Classifier comparison

Compare Stochastic learning strategies for MLPClassifier

Compare Stochastic learning strategies for MLPClassifier

Varying regularization in Multi-layer Perceptron

Varying regularization in Multi-layer Perceptron

Visualization of MLP weights on MNIST

Visualization of MLP weights on MNIST