8.14.1.18. 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=False, copy_X=True, verbose=False)¶

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)

Parameters :

X : array, shape = (n_samples, n_features)

Training vectors.

y : array, shape = (n_samples)

Target values for training vectors

n_iter : int, optional

Maximum number of iterations. Default is 300

tol : float, optional

Stop the algorithm if w has converged. Default is 1.e-3.

alpha_1 : float, optional

Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.

alpha_2 : float, optional

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.

lambda_1 : float, optional

Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.

lambda_2 : float, optional

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.

compute_score : boolean, optional

If True, compute the objective function at each step of the model. Default is False.

threshold_lambda : float, optional

threshold for removing (pruning) weights with high precision from the computation. Default is 1.e+4.

fit_intercept : boolean, optional

wether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). Default is True.

normalize : boolean, optional

If True, the regressors X are normalized

copy_X : boolean, optional, default True.

If True, X will be copied; else, it may be overwritten.

verbose : boolean, optional, default False

Verbose mode when fitting the model.

Notes

See examples/linear_model/plot_ard.py for an example.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.ARDRegression()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
... 
ARDRegression(alpha_1=1e-06, alpha_2=1e-06, compute_score=False,
        copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06,
        n_iter=300, normalize=False, threshold_lambda=10000.0, tol=0.001,
        verbose=False)
>>> clf.predict([[1, 1]])
array([ 1.])

Attributes

coef_	array, shape = (n_features)	Coefficients of the regression model (mean of distribution)
alpha_	float	estimated precision of the noise.
lambda_	array, shape = (n_features)	estimated precisions of the weights.
sigma_	array, shape = (n_features, n_features)	estimated variance-covariance matrix of the weights
scores_	float	if computed, value of the objective function (to be maximized)

Methods

`decision_function`(X)	Decision function of the linear model
`fit`(X, y)	Fit the ARDRegression model according to the given training data
`predict`(X)	Predict using the linear model
`score`(X, y)	Returns the coefficient of determination R^2 of the prediction.
`set_params`(**params)	Set the parameters of the estimator.

__init__(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=False, copy_X=True, verbose=False)¶

decision_function(X)¶

Decision function of the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

fit(X, y)¶

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

Iterative procedure to maximize the evidence

Parameters :

X : array-like, shape = [n_samples, n_features]

Training vector, where n_samples in the number of samples and n_features is the number of features.

y : array, shape = [n_samples]

Target values (integers)

Returns :

self : returns an instance of self.

predict(X)¶

Predict using the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

score(X, y)¶

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 - 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, lower values are worse.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float

set_params(**params)¶

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :	self :

Citing

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8.14.1.18. sklearn.linear_model.ARDRegression¶