module mlmodel.quantile_mlpregressor

Inheritance diagram of mlinsights.mlmodel.quantile_mlpregressor

Short summary

module mlinsights.mlmodel.quantile_mlpregressor

Implements a quantile non-linear regression.

source on GitHub

Classes

class

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CustomizedMultilayerPerceptron

Customized MLP Perceptron based on BaseMultilayerPerceptron. …

QuantileMLPRegressor

Quantile MLP Regression or neural networks regression trained with norm L1. This class inherits from sklearn.neural_networks.MLPRegressor. …

Functions

function

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absolute_loss

Computes the absolute loss for regression. Parameters ———- y_true : array-like or label indicator matrix …

float_sign

Returns 1 if a > 0, otherwise -1

Properties

property

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partial_fit

Update the model with a single iteration over the given data. Parameters ———- X : {array-like, …

partial_fit

Update the model with a single iteration over the given data. Parameters ———- X : {array-like, …

Methods

method

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__init__

__init__

Parameters ———- See sklearn.neural_networks.MLPRegressor

_backprop

Computes the MLP loss function and its corresponding derivatives with respect to each parameter: weights and bias …

_backprop

Computes the MLP loss function and its corresponding derivatives with respect to each parameter: weights and bias …

_get_loss_function

Returns the loss functions.

_get_loss_function

Returns the loss functions.

_modify_loss_derivatives

Modifies the loss derivatives.

_modify_loss_derivatives

Modifies the loss derivatives.

_validate_input

predict

Predicts using the multi-layer perceptron model. Parameters ———- X : {array-like, sparse …

score

Returns mean absolute error regression loss. Parameters ———- X : array-like, shape = (n_samples, …

Documentation

Implements a quantile non-linear regression.

source on GitHub

class mlinsights.mlmodel.quantile_mlpregressor.CustomizedMultilayerPerceptron(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, n_iter_no_change)[source]

Bases: sklearn.neural_network.multilayer_perceptron.BaseMultilayerPerceptron

Customized MLP Perceptron based on BaseMultilayerPerceptron.

source on GitHub

__abstractmethods__ = frozenset({})
__init__(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, n_iter_no_change)[source]

Initialize self. See help(type(self)) for accurate signature.

_abc_impl = <_abc_data object>
_backprop(X, y, activations, deltas, coef_grads, intercept_grads)[source]

Computes 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_grads (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)

source on GitHub

_get_loss_function(loss_func_name)[source]

Returns the loss functions.

Parameters

loss_func_name – loss function name, see sklearn.neural_networks.MLPRegressor

source on GitHub

_modify_loss_derivatives(last_deltas)[source]

Modifies the loss derivatives.

Parameters

last_deltas – last deltas is the difference between the output and the expected output

Returns

modified derivatives

source on GitHub

class mlinsights.mlmodel.quantile_mlpregressor.QuantileMLPRegressor(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)[source]

Bases: mlinsights.mlmodel.quantile_mlpregressor.CustomizedMultilayerPerceptron, sklearn.base.RegressorMixin

Quantile MLP Regression or neural networks regression trained with norm L1. This class inherits from sklearn.neural_networks.MLPRegressor. This model optimizes the absolute-loss using LBFGS or stochastic gradient descent. See CustomizedMultilayerPerceptron and absolute_loss.

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’.

  • 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’.

  • max_iter (int, optional, 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, optional, default True) – Whether to shuffle samples in each iteration. Only used when solver=’sgd’ or ‘adam’.

  • random_state (int, RandomState instance or None, optional, default None) – If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

  • tol (float, optional, 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, 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. 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 (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 n_iter_no_change 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’

  • n_iter_no_change (int, optional, default 10) – Maximum number of epochs to not meet tol improvement. Only effective when solver=’sgd’ or ‘adam’ .. versionadded:: 0.20

loss_

The current loss computed with the loss function.

Type

float

coefs_

The ith element in the list represents the weight matrix corresponding to layer i.

Type

list, length n_layers - 1

intercepts_

The ith element in the list represents the bias vector corresponding to layer i + 1.

Type

list, length n_layers - 1

n_iter_

The number of iterations the solver has ran.

Type

int,

n_layers_

Number of layers.

Type

int

n_outputs_

Number of outputs.

Type

int

out_activation_

Name of the output activation function.

Type

string

Notes

QuantileMLPRegressor 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).

source on GitHub

:param See sklearn.neural_networks.MLPRegressor:

source on GitHub

__abstractmethods__ = frozenset({})
__init__(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)[source]

:param See sklearn.neural_networks.MLPRegressor:

source on GitHub

_abc_impl = <_abc_data object>
_validate_input(X, y, incremental)[source]
predict(X)[source]

Predicts using the multi-layer perceptron model.

Parameters

X ({array-like, sparse matrix}, shape (n_samples, n_features)) – The input data.

Returns

y – The predicted values.

Return type

array-like, shape (n_samples, n_outputs)

source on GitHub

score(X, y, sample_weight=None)[source]

Returns mean absolute error regression loss.

Parameters
  • X (array-like, shape = (n_samples, n_features)) – Test samples.

  • y (array-like, shape = (n_samples) or (n_samples, n_outputs)) – True values for X.

  • sample_weight (array-like, shape = [n_samples], optional) – Sample weights.

Returns

score – mean absolute error regression loss

Return type

float

source on GitHub

mlinsights.mlmodel.quantile_mlpregressor.absolute_loss(y_true, y_pred)[source]

Computes the absolute loss for regression.

Parameters
  • y_true (array-like or label indicator matrix) – Ground truth (correct) values.

  • y_pred (array-like or label indicator matrix) – Predicted values, as returned by a regression estimator.

Returns

loss – The degree to which the samples are correctly predicted.

Return type

float

source on GitHub

mlinsights.mlmodel.quantile_mlpregressor.float_sign(a)[source]

Returns 1 if a > 0, otherwise -1