"""Multi-layer Perceptron """ # Authors: Issam H. Laradji # Andreas Mueller # Jiyuan Qian # License: BSD 3 clause import numpy as np from abc import ABCMeta, abstractmethod from scipy.optimize import fmin_l_bfgs_b import warnings from ..base import BaseEstimator, ClassifierMixin, RegressorMixin from ._base import ACTIVATIONS, DERIVATIVES, LOSS_FUNCTIONS from ._stochastic_optimizers import SGDOptimizer, AdamOptimizer from ..model_selection import train_test_split from ..externals import six from ..preprocessing import LabelBinarizer from ..utils import gen_batches, check_random_state from ..utils import shuffle from ..utils import check_array, check_X_y, column_or_1d from ..exceptions import ConvergenceWarning from ..utils.extmath import safe_sparse_dot from ..utils.validation import check_is_fitted from ..utils.multiclass import _check_partial_fit_first_call, unique_labels from ..utils.multiclass import type_of_target _STOCHASTIC_SOLVERS = ['sgd', 'adam'] def _pack(coefs_, intercepts_): """Pack the parameters into a single vector.""" return np.hstack([l.ravel() for l in coefs_ + intercepts_]) class BaseMultilayerPerceptron(six.with_metaclass(ABCMeta, BaseEstimator)): """Base class for MLP classification and regression. Warning: This class should not be used directly. Use derived classes instead. .. versionadded:: 0.18 """ @abstractmethod def __init__(self, hidden_layer_sizes, activation, solver, alpha, batch_size, learning_rate, learning_rate_init, power_t, max_iter, loss, shuffle, random_state, tol, verbose, warm_start, momentum, nesterovs_momentum, early_stopping, validation_fraction, beta_1, beta_2, epsilon): self.activation = activation self.solver = solver self.alpha = alpha self.batch_size = batch_size self.learning_rate = learning_rate self.learning_rate_init = learning_rate_init self.power_t = power_t self.max_iter = max_iter self.loss = loss self.hidden_layer_sizes = hidden_layer_sizes self.shuffle = shuffle self.random_state = random_state self.tol = tol self.verbose = verbose self.warm_start = warm_start self.momentum = momentum self.nesterovs_momentum = nesterovs_momentum self.early_stopping = early_stopping self.validation_fraction = validation_fraction self.beta_1 = beta_1 self.beta_2 = beta_2 self.epsilon = epsilon def _unpack(self, packed_parameters): """Extract the coefficients and intercepts from packed_parameters.""" for i in range(self.n_layers_ - 1): start, end, shape = self._coef_indptr[i] self.coefs_[i] = np.reshape(packed_parameters[start:end], shape) start, end = self._intercept_indptr[i] self.intercepts_[i] = packed_parameters[start:end] def _forward_pass(self, activations): """Perform a forward pass on the network by computing the values of the neurons in the hidden layers and the output layer. Parameters ---------- activations: list, length = n_layers - 1 The ith element of the list holds the values of the ith layer. with_output_activation : bool, default True If True, the output passes through the output activation function, which is either the softmax function or the logistic function """ hidden_activation = ACTIVATIONS[self.activation] # Iterate over the hidden layers for i in range(self.n_layers_ - 1): activations[i + 1] = safe_sparse_dot(activations[i], self.coefs_[i]) activations[i + 1] += self.intercepts_[i] # For the hidden layers if (i + 1) != (self.n_layers_ - 1): activations[i + 1] = hidden_activation(activations[i + 1]) # For the last layer output_activation = ACTIVATIONS[self.out_activation_] activations[i + 1] = output_activation(activations[i + 1]) return activations def _compute_loss_grad(self, layer, n_samples, activations, deltas, coef_grads, intercept_grads): """Compute the gradient of loss with respect to coefs and intercept for specified layer. This function does backpropagation for the specified one layer. """ coef_grads[layer] = safe_sparse_dot(activations[layer].T, deltas[layer]) coef_grads[layer] += (self.alpha * self.coefs_[layer]) coef_grads[layer] /= n_samples intercept_grads[layer] = np.mean(deltas[layer], 0) return coef_grads, intercept_grads def _loss_grad_lbfgs(self, packed_coef_inter, X, y, activations, deltas, coef_grads, intercept_grads): """Compute the MLP loss function and its corresponding derivatives with respect to the different parameters given in the initialization. Returned gradients are packed in a single vector so it can be used in lbfgs Parameters ---------- packed_parameters : array-like A vector comprising the flattened coefficients and intercepts. X : {array-like, sparse matrix}, shape (n_samples, n_features) The input data. y : array-like, shape (n_samples,) The target values. activations: list, length = n_layers - 1 The ith element of the list holds the values of the ith layer. deltas : list, length = n_layers - 1 The ith element of the list holds the difference between the activations of the i + 1 layer and the backpropagated error. More specifically, deltas are gradients of loss with respect to z in each layer, where z = wx + b is the value of a particular layer before passing through the activation function coef_grad : list, length = n_layers - 1 The ith element contains the amount of change used to update the coefficient parameters of the ith layer in an iteration. intercept_grads : list, length = n_layers - 1 The ith element contains the amount of change used to update the intercept parameters of the ith layer in an iteration. Returns ------- loss : float grad : array-like, shape (number of nodes of all layers,) """ self._unpack(packed_coef_inter) loss, coef_grads, intercept_grads = self._backprop( X, y, activations, deltas, coef_grads, intercept_grads) self.n_iter_ += 1 grad = _pack(coef_grads, intercept_grads) return loss, grad def _backprop(self, X, y, activations, deltas, coef_grads, intercept_grads): """Compute the MLP loss function and its corresponding derivatives with respect to each parameter: weights and bias vectors. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) The input data. y : array-like, shape (n_samples,) The target values. activations: list, length = n_layers - 1 The ith element of the list holds the values of the ith layer. deltas : list, length = n_layers - 1 The ith element of the list holds the difference between the activations of the i + 1 layer and the backpropagated error. More specifically, deltas are gradients of loss with respect to z in each layer, where z = wx + b is the value of a particular layer before passing through the activation function coef_grad : list, length = n_layers - 1 The ith element contains the amount of change used to update the coefficient parameters of the ith layer in an iteration. intercept_grads : list, length = n_layers - 1 The ith element contains the amount of change used to update the intercept parameters of the ith layer in an iteration. Returns ------- loss : float coef_grads : list, length = n_layers - 1 intercept_grads : list, length = n_layers - 1 """ n_samples = X.shape[0] # Forward propagate activations = self._forward_pass(activations) # Get loss loss_func_name = self.loss if loss_func_name == 'log_loss' and self.out_activation_ == 'logistic': loss_func_name = 'binary_log_loss' loss = LOSS_FUNCTIONS[loss_func_name](y, activations[-1]) # Add L2 regularization term to loss values = np.sum( np.array([np.dot(s.ravel(), s.ravel()) for s in self.coefs_])) loss += (0.5 * self.alpha) * values / n_samples # Backward propagate last = self.n_layers_ - 2 # The calculation of delta[last] here works with following # combinations of output activation and loss function: # sigmoid and binary cross entropy, softmax and categorical cross # entropy, and identity with squared loss deltas[last] = activations[-1] - y # Compute gradient for the last layer coef_grads, intercept_grads = self._compute_loss_grad( last, n_samples, activations, deltas, coef_grads, intercept_grads) # Iterate over the hidden layers for i in range(self.n_layers_ - 2, 0, -1): deltas[i - 1] = safe_sparse_dot(deltas[i], self.coefs_[i].T) inplace_derivative = DERIVATIVES[self.activation] inplace_derivative(activations[i], deltas[i - 1]) coef_grads, intercept_grads = self._compute_loss_grad( i - 1, n_samples, activations, deltas, coef_grads, intercept_grads) return loss, coef_grads, intercept_grads def _initialize(self, y, layer_units): # set all attributes, allocate weights etc for first call # Initialize parameters self.n_iter_ = 0 self.t_ = 0 self.n_outputs_ = y.shape[1] # Compute the number of layers self.n_layers_ = len(layer_units) # Output for regression if not isinstance(self, ClassifierMixin): self.out_activation_ = 'identity' # Output for multi class elif self._label_binarizer.y_type_ == 'multiclass': self.out_activation_ = 'softmax' # Output for binary class and multi-label else: self.out_activation_ = 'logistic' # Initialize coefficient and intercept layers self.coefs_ = [] self.intercepts_ = [] for i in range(self.n_layers_ - 1): coef_init, intercept_init = self._init_coef(layer_units[i], layer_units[i + 1]) self.coefs_.append(coef_init) self.intercepts_.append(intercept_init) if self.solver in _STOCHASTIC_SOLVERS: self.loss_curve_ = [] self._no_improvement_count = 0 if self.early_stopping: self.validation_scores_ = [] self.best_validation_score_ = -np.inf else: self.best_loss_ = np.inf def _init_coef(self, fan_in, fan_out): if self.activation == 'logistic': # Use the initialization method recommended by # Glorot et al. init_bound = np.sqrt(2. / (fan_in + fan_out)) elif self.activation in ('identity', 'tanh', 'relu'): init_bound = np.sqrt(6. / (fan_in + fan_out)) else: # this was caught earlier, just to make sure raise ValueError("Unknown activation function %s" % self.activation) coef_init = self._random_state.uniform(-init_bound, init_bound, (fan_in, fan_out)) intercept_init = self._random_state.uniform(-init_bound, init_bound, fan_out) return coef_init, intercept_init def _fit(self, X, y, incremental=False): # Make sure self.hidden_layer_sizes is a list hidden_layer_sizes = self.hidden_layer_sizes if not hasattr(hidden_layer_sizes, "__iter__"): hidden_layer_sizes = [hidden_layer_sizes] hidden_layer_sizes = list(hidden_layer_sizes) # Validate input parameters. self._validate_hyperparameters() if np.any(np.array(hidden_layer_sizes) <= 0): raise ValueError("hidden_layer_sizes must be > 0, got %s." % hidden_layer_sizes) X, y = self._validate_input(X, y, incremental) n_samples, n_features = X.shape # Ensure y is 2D if y.ndim == 1: y = y.reshape((-1, 1)) self.n_outputs_ = y.shape[1] layer_units = ([n_features] + hidden_layer_sizes + [self.n_outputs_]) # check random state self._random_state = check_random_state(self.random_state) if not hasattr(self, 'coefs_') or (not self.warm_start and not incremental): # First time training the model self._initialize(y, layer_units) # lbfgs does not support mini-batches if self.solver == 'lbfgs': batch_size = n_samples elif self.batch_size == 'auto': batch_size = min(200, n_samples) else: if self.batch_size < 1 or self.batch_size > n_samples: warnings.warn("Got `batch_size` less than 1 or larger than " "sample size. It is going to be clipped") batch_size = np.clip(self.batch_size, 1, n_samples) # Initialize lists activations = [X] activations.extend(np.empty((batch_size, n_fan_out)) for n_fan_out in layer_units[1:]) deltas = [np.empty_like(a_layer) for a_layer in activations] coef_grads = [np.empty((n_fan_in_, n_fan_out_)) for n_fan_in_, n_fan_out_ in zip(layer_units[:-1], layer_units[1:])] intercept_grads = [np.empty(n_fan_out_) for n_fan_out_ in layer_units[1:]] # Run the Stochastic optimization solver if self.solver in _STOCHASTIC_SOLVERS: self._fit_stochastic(X, y, activations, deltas, coef_grads, intercept_grads, layer_units, incremental) # Run the LBFGS solver elif self.solver == 'lbfgs': self._fit_lbfgs(X, y, activations, deltas, coef_grads, intercept_grads, layer_units) return self def _validate_hyperparameters(self): if not isinstance(self.shuffle, bool): raise ValueError("shuffle must be either True or False, got %s." % self.shuffle) if self.max_iter <= 0: raise ValueError("max_iter must be > 0, got %s." % self.max_iter) if self.alpha < 0.0: raise ValueError("alpha must be >= 0, got %s." % self.alpha) if (self.learning_rate in ["constant", "invscaling", "adaptive"] and self.learning_rate_init <= 0.0): raise ValueError("learning_rate_init must be > 0, got %s." % self.learning_rate) if self.momentum > 1 or self.momentum < 0: raise ValueError("momentum must be >= 0 and <= 1, got %s" % self.momentum) if not isinstance(self.nesterovs_momentum, bool): raise ValueError("nesterovs_momentum must be either True or False," " got %s." % self.nesterovs_momentum) if not isinstance(self.early_stopping, bool): raise ValueError("early_stopping must be either True or False," " got %s." % self.early_stopping) if self.validation_fraction < 0 or self.validation_fraction >= 1: raise ValueError("validation_fraction must be >= 0 and < 1, " "got %s" % self.validation_fraction) if self.beta_1 < 0 or self.beta_1 >= 1: raise ValueError("beta_1 must be >= 0 and < 1, got %s" % self.beta_1) if self.beta_2 < 0 or self.beta_2 >= 1: raise ValueError("beta_2 must be >= 0 and < 1, got %s" % self.beta_2) if self.epsilon <= 0.0: raise ValueError("epsilon must be > 0, got %s." % self.epsilon) # raise ValueError if not registered supported_activations = ('identity', 'logistic', 'tanh', 'relu') if self.activation not in supported_activations: raise ValueError("The activation '%s' is not supported. Supported " "activations are %s." % (self.activation, supported_activations)) if self.learning_rate not in ["constant", "invscaling", "adaptive"]: raise ValueError("learning rate %s is not supported. " % self.learning_rate) supported_solvers = _STOCHASTIC_SOLVERS + ["lbfgs"] if self.solver not in supported_solvers: raise ValueError("The solver %s is not supported. " " Expected one of: %s" % (self.solver, ", ".join(supported_solvers))) def _fit_lbfgs(self, X, y, activations, deltas, coef_grads, intercept_grads, layer_units): # Store meta information for the parameters self._coef_indptr = [] self._intercept_indptr = [] start = 0 # Save sizes and indices of coefficients for faster unpacking for i in range(self.n_layers_ - 1): n_fan_in, n_fan_out = layer_units[i], layer_units[i + 1] end = start + (n_fan_in * n_fan_out) self._coef_indptr.append((start, end, (n_fan_in, n_fan_out))) start = end # Save sizes and indices of intercepts for faster unpacking for i in range(self.n_layers_ - 1): end = start + layer_units[i + 1] self._intercept_indptr.append((start, end)) start = end # Run LBFGS packed_coef_inter = _pack(self.coefs_, self.intercepts_) if self.verbose is True or self.verbose >= 1: iprint = 1 else: iprint = -1 optimal_parameters, self.loss_, d = fmin_l_bfgs_b( x0=packed_coef_inter, func=self._loss_grad_lbfgs, maxfun=self.max_iter, iprint=iprint, pgtol=self.tol, args=(X, y, activations, deltas, coef_grads, intercept_grads)) self._unpack(optimal_parameters) def _fit_stochastic(self, X, y, activations, deltas, coef_grads, intercept_grads, layer_units, incremental): if not incremental or not hasattr(self, '_optimizer'): params = self.coefs_ + self.intercepts_ if self.solver == 'sgd': self._optimizer = SGDOptimizer( params, self.learning_rate_init, self.learning_rate, self.momentum, self.nesterovs_momentum, self.power_t) elif self.solver == 'adam': self._optimizer = AdamOptimizer( params, self.learning_rate_init, self.beta_1, self.beta_2, self.epsilon) # early_stopping in partial_fit doesn't make sense early_stopping = self.early_stopping and not incremental if early_stopping: X, X_val, y, y_val = train_test_split( X, y, random_state=self._random_state, test_size=self.validation_fraction) if isinstance(self, ClassifierMixin): y_val = self._label_binarizer.inverse_transform(y_val) else: X_val = None y_val = None n_samples = X.shape[0] if self.batch_size == 'auto': batch_size = min(200, n_samples) else: batch_size = np.clip(self.batch_size, 1, n_samples) try: for it in range(self.max_iter): X, y = shuffle(X, y, random_state=self._random_state) accumulated_loss = 0.0 for batch_slice in gen_batches(n_samples, batch_size): activations[0] = X[batch_slice] batch_loss, coef_grads, intercept_grads = self._backprop( X[batch_slice], y[batch_slice], activations, deltas, coef_grads, intercept_grads) accumulated_loss += batch_loss * (batch_slice.stop - batch_slice.start) # update weights grads = coef_grads + intercept_grads self._optimizer.update_params(grads) self.n_iter_ += 1 self.loss_ = accumulated_loss / X.shape[0] self.t_ += n_samples self.loss_curve_.append(self.loss_) if self.verbose: print("Iteration %d, loss = %.8f" % (self.n_iter_, self.loss_)) # update no_improvement_count based on training loss or # validation score according to early_stopping self._update_no_improvement_count(early_stopping, X_val, y_val) # for learning rate that needs to be updated at iteration end self._optimizer.iteration_ends(self.t_) if self._no_improvement_count > 2: # not better than last two iterations by tol. # stop or decrease learning rate if early_stopping: msg = ("Validation score did not improve more than " "tol=%f for two consecutive epochs." % self.tol) else: msg = ("Training loss did not improve more than tol=%f" " for two consecutive epochs." % self.tol) is_stopping = self._optimizer.trigger_stopping( msg, self.verbose) if is_stopping: break else: self._no_improvement_count = 0 if incremental: break if self.n_iter_ == self.max_iter: warnings.warn('Stochastic Optimizer: Maximum iterations' ' reached and the optimization hasn\'t ' 'converged yet.' % (), ConvergenceWarning) except KeyboardInterrupt: pass if early_stopping: # restore best weights self.coefs_ = self._best_coefs self.intercepts_ = self._best_intercepts def _update_no_improvement_count(self, early_stopping, X_val, y_val): if early_stopping: # compute validation score, use that for stopping self.validation_scores_.append(self.score(X_val, y_val)) if self.verbose: print("Validation score: %f" % self.validation_scores_[-1]) # update best parameters # use validation_scores_, not loss_curve_ # let's hope no-one overloads .score with mse last_valid_score = self.validation_scores_[-1] if last_valid_score < (self.best_validation_score_ + self.tol): self._no_improvement_count += 1 else: self._no_improvement_count = 0 if last_valid_score > self.best_validation_score_: self.best_validation_score_ = last_valid_score self._best_coefs = [c.copy() for c in self.coefs_] self._best_intercepts = [i.copy() for i in self.intercepts_] else: if self.loss_curve_[-1] > self.best_loss_ - self.tol: self._no_improvement_count += 1 else: self._no_improvement_count = 0 if self.loss_curve_[-1] < self.best_loss_: self.best_loss_ = self.loss_curve_[-1] def fit(self, 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. """ return self._fit(X, y, incremental=False) @property def partial_fit(self): """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. """ if self.solver not in _STOCHASTIC_SOLVERS: raise AttributeError("partial_fit is only available for stochastic" " optimizers. %s is not stochastic." % self.solver) return self._partial_fit def _partial_fit(self, X, y, classes=None): return self._fit(X, y, incremental=True) def _predict(self, X): """Predict using the trained model Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) The input data. Returns ------- y_pred : array-like, shape (n_samples,) or (n_samples, n_outputs) The decision function of the samples for each class in the model. """ X = check_array(X, accept_sparse=['csr', 'csc', 'coo']) # Make sure self.hidden_layer_sizes is a list hidden_layer_sizes = self.hidden_layer_sizes if not hasattr(hidden_layer_sizes, "__iter__"): hidden_layer_sizes = [hidden_layer_sizes] hidden_layer_sizes = list(hidden_layer_sizes) layer_units = [X.shape[1]] + hidden_layer_sizes + \ [self.n_outputs_] # Initialize layers activations = [X] for i in range(self.n_layers_ - 1): activations.append(np.empty((X.shape[0], layer_units[i + 1]))) # forward propagate self._forward_pass(activations) y_pred = activations[-1] return y_pred class MLPClassifier(BaseMultilayerPerceptron, ClassifierMixin): """Multi-layer Perceptron classifier. This model optimizes the log-loss function using LBFGS or stochastic gradient descent. .. versionadded:: 0.18 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 : {'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, optional, default 0.0001 L2 penalty (regularization term) parameter. batch_size : int, optional, 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'``. max_iter : int, optional, default 200 Maximum number of iterations. The solver 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 solver='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 solver='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 solver='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 solver='sgd'. nesterovs_momentum : boolean, 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 two consecutive epochs. Only effective when solver='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 solver='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 solver='adam' epsilon : float, optional, default 1e-8 Value for numerical stability in adam. Only used when solver='adam' Attributes ---------- `classes_` : array or list of array of shape (n_classes,) Class labels for each output. `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 solver has ran. n_layers_ : int Number of layers. `n_outputs_` : int Number of outputs. `out_activation_` : string Name of the output activation function. 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. "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). """ def __init__(self, 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=1e-4, 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-8): sup = super(MLPClassifier, self) sup.__init__(hidden_layer_sizes=hidden_layer_sizes, activation=activation, solver=solver, alpha=alpha, batch_size=batch_size, learning_rate=learning_rate, learning_rate_init=learning_rate_init, power_t=power_t, max_iter=max_iter, loss='log_loss', shuffle=shuffle, random_state=random_state, tol=tol, verbose=verbose, warm_start=warm_start, momentum=momentum, nesterovs_momentum=nesterovs_momentum, early_stopping=early_stopping, validation_fraction=validation_fraction, beta_1=beta_1, beta_2=beta_2, epsilon=epsilon) def _validate_input(self, X, y, incremental): X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'], multi_output=True) if y.ndim == 2 and y.shape[1] == 1: y = column_or_1d(y, warn=True) if not incremental: self._label_binarizer = LabelBinarizer() self._label_binarizer.fit(y) self.classes_ = self._label_binarizer.classes_ else: classes = unique_labels(y) if np.setdiff1d(classes, self.classes_, assume_unique=True): raise ValueError("`y` has classes not in `self.classes_`." " `self.classes_` has %s. 'y' has %s." % (self.classes_, classes)) y = self._label_binarizer.transform(y) return X, y def predict(self, X): """Predict using the multi-layer perceptron classifier Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) The input data. Returns ------- y : array-like, shape (n_samples,) or (n_samples, n_classes) The predicted classes. """ check_is_fitted(self, "coefs_") y_pred = self._predict(X) if self.n_outputs_ == 1: y_pred = y_pred.ravel() return self._label_binarizer.inverse_transform(y_pred) @property def partial_fit(self): """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. classes : array, shape (n_classes) 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 : returns a trained MLP model. """ if self.solver not in _STOCHASTIC_SOLVERS: raise AttributeError("partial_fit is only available for stochastic" " optimizer. %s is not stochastic" % self.solver) return self._partial_fit def _partial_fit(self, X, y, classes=None): if _check_partial_fit_first_call(self, classes): self._label_binarizer = LabelBinarizer() if type_of_target(y).startswith('multilabel'): self._label_binarizer.fit(y) else: self._label_binarizer.fit(classes) super(MLPClassifier, self)._partial_fit(X, y) return self def predict_log_proba(self, X): """Return the log of probability estimates. Parameters ---------- X : array-like, shape (n_samples, n_features) The input data. Returns ------- log_y_prob : array-like, 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)) """ y_prob = self.predict_proba(X) return np.log(y_prob, out=y_prob) def predict_proba(self, X): """Probability estimates. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) The input data. Returns ------- y_prob : array-like, 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_`. """ check_is_fitted(self, "coefs_") y_pred = self._predict(X) if self.n_outputs_ == 1: y_pred = y_pred.ravel() if y_pred.ndim == 1: return np.vstack([1 - y_pred, y_pred]).T else: return y_pred class MLPRegressor(BaseMultilayerPerceptron, RegressorMixin): """Multi-layer Perceptron regressor. This model optimizes the squared-loss using LBFGS or stochastic gradient descent. .. versionadded:: 0.18 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 : {'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, optional, default 0.0001 L2 penalty (regularization term) parameter. batch_size : int, optional, 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'. max_iter : int, optional, default 200 Maximum number of iterations. The solver 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 solver='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 solver='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 solver='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 solver='sgd'. nesterovs_momentum : boolean, 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 two consecutive epochs. Only effective when solver='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 solver='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 solver='adam' epsilon : float, optional, default 1e-8 Value for numerical stability in adam. Only used when solver='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 solver 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). """ def __init__(self, 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=1e-4, 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-8): sup = super(MLPRegressor, self) sup.__init__(hidden_layer_sizes=hidden_layer_sizes, activation=activation, solver=solver, alpha=alpha, batch_size=batch_size, learning_rate=learning_rate, learning_rate_init=learning_rate_init, power_t=power_t, max_iter=max_iter, loss='squared_loss', shuffle=shuffle, random_state=random_state, tol=tol, verbose=verbose, warm_start=warm_start, momentum=momentum, nesterovs_momentum=nesterovs_momentum, early_stopping=early_stopping, validation_fraction=validation_fraction, beta_1=beta_1, beta_2=beta_2, epsilon=epsilon) def predict(self, 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. """ check_is_fitted(self, "coefs_") y_pred = self._predict(X) if y_pred.shape[1] == 1: return y_pred.ravel() return y_pred def _validate_input(self, X, y, incremental): X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'], multi_output=True, y_numeric=True) if y.ndim == 2 and y.shape[1] == 1: y = column_or_1d(y, warn=True) return X, y