`sklearn.linear_model`.ARDRegression¶

class sklearn.linear_model.ARDRegression(*, n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, threshold_lambda=10000.0, fit_intercept=True, normalize='deprecated', copy_X=True, verbose=False)[source]¶

Bayesian ARD regression.

Fit the weights of a regression model, using an ARD prior. The weights of the regression model are assumed to be in Gaussian distributions. Also estimate the parameters lambda (precisions of the distributions of the weights) and alpha (precision of the distribution of the noise). The estimation is done by an iterative procedures (Evidence Maximization)

See also

BayesianRidge: Bayesian ridge regression.

Notes

For an example, see examples/linear_model/plot_ard.py.

References

D. J. C. MacKay, Bayesian nonlinear modeling for the prediction competition, ASHRAE Transactions, 1994.

R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our self.alpha_ Their alpha is our self.lambda_ ARD is a little different than the slide: only dimensions/features for which self.lambda_ < self.threshold_lambda are kept and the rest are discarded.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.ARDRegression()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
ARDRegression()
>>> clf.predict([[1, 1]])
array([1.])

Methods

`fit`(X, y)	Fit the model according to the given training data and parameters.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X[, return_std])	Predict using the linear model.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y)[source]¶

Fit the model according to the given training data and parameters.

Iterative procedure to maximize the evidence

Parameters

Xarray-like of shape (n_samples, n_features): Training vector, where n_samples is the number of samples and n_features is the number of features.
yarray-like of shape (n_samples,): Target values (integers). Will be cast to X’s dtype if necessary.

Returns

selfobject: Fitted estimator.

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

paramsdict: Parameter names mapped to their values.

predict(X, return_std=False)[source]¶

Predict using the linear model.

In addition to the mean of the predictive distribution, also its standard deviation can be returned.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): Samples.
return_stdbool, default=False: Whether to return the standard deviation of posterior prediction.

Returns

y_meanarray-like of shape (n_samples,): Mean of predictive distribution of query points.
y_stdarray-like of shape (n_samples,): Standard deviation of predictive distribution of query points.

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

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The 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

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True values for X.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns

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

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)[source]¶

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

**paramsdict: Estimator parameters.

Returns

selfestimator instance: Estimator instance.

Examples using `sklearn.linear_model.ARDRegression`¶

sklearn.linear_model.ARDRegression¶

Examples using sklearn.linear_model.ARDRegression¶

`sklearn.linear_model`.ARDRegression¶

Examples using `sklearn.linear_model.ARDRegression`¶