polylearn.PolynomialNetworkRegressor¶

class polylearn.PolynomialNetworkRegressor(degree=2, n_components=2, beta=1, tol=1e-06, fit_lower=’augment’, warm_start=False, max_iter=10000, verbose=False, random_state=None)[source]¶

Polynomial network for regression (with squared loss).

Parameters:

degree : int >= 2, default: 2 Degree of the polynomial. Corresponds to the order of feature interactions captured by the model. Currently only supports degrees up to 3. n_components : int, default: 2 Dimension of the lifted tensor. beta : float, default: 1 Regularization amount for higher-order weights. tol : float, default: 1e-6 Tolerance for the stopping condition. fit_lower : {‘augment’|None}, default: ‘augment’ Whether and how to fit lower-order, non-homogeneous terms. ‘augment’: adds a dummy column (1 everywhere) in order to capture lower-order terms (including linear terms). None: only learns weights for the degree given. warm_start : boolean, optional, default: False Whether to use the existing solution, if available. Useful for computing regularization paths or pre-initializing the model. max_iter : int, optional, default: 10000 Maximum number of passes over the dataset to perform. verbose : boolean, optional, default: False Whether to print debugging information. random_state : int seed, RandomState instance, or None (default) The seed of the pseudo random number generator to use for initializing the parameters.

Attributes:

self.U_ : array, shape [n_components, n_features, degree] The learned weights in the lifted tensor parametrization.

References

Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms. Mathieu Blondel, Masakazu Ishihata, Akinori Fujino, Naonori Ueda. In: Proceedings of ICML 2016. http://mblondel.org/publications/mblondel-icml2016.pdf

On the computational efficiency of training neural networks. Roi Livni, Shai Shalev-Shwartz, Ohad Shamir. In: Proceedings of NIPS 2014.

Methods

fit(X, y)	Fit polynomial network to training data.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict regression output for the samples in X.
score(X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of this estimator.

__init__(degree=2, n_components=2, beta=1, tol=1e-06, fit_lower=’augment’, warm_start=False, max_iter=10000, verbose=False, random_state=None)[source]¶

fit(X, y)¶

Fit polynomial network to training data.

Parameters:	X : array-like or sparse, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of features. y : array-like, shape = [n_samples] Target values.
Returns:	self : Estimator Returns self.

get_params(deep=True)¶

Get parameters for this estimator.

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping of string to any Parameter names mapped to their values.

predict(X)¶

Predict regression output for the samples in X.

Parameters:	X : {array-like, sparse matrix}, shape = [n_samples, n_features] Samples.
Returns:	y_pred : array, shape = [n_samples] Returns predicted values.

score(X, y, sample_weight=None)¶

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

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 : float R^2 of self.predict(X) wrt. y.

set_params(**params)¶

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.

Returns:	self :