ARDRegression (original) (raw)

class sklearn.linear_model.ARDRegression(*, max_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, 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)

Read more in the User Guide.

Parameters:

max_iterint, default=300

Maximum number of iterations.

Changed in version 1.3.

tolfloat, default=1e-3

Stop the algorithm if w has converged.

alpha_1float, default=1e-6

Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter.

alpha_2float, default=1e-6

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter.

lambda_1float, default=1e-6

Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter.

lambda_2float, default=1e-6

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter.

compute_scorebool, default=False

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

threshold_lambdafloat, default=10 000

Threshold for removing (pruning) weights with high precision from the computation.

fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).

copy_Xbool, default=True

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

verbosebool, default=False

Verbose mode when fitting the model.

Attributes:

**coef_**array-like of shape (n_features,)

Coefficients of the regression model (mean of distribution)

**alpha_**float

estimated precision of the noise.

**lambda_**array-like of shape (n_features,)

estimated precisions of the weights.

**sigma_**array-like of shape (n_features, n_features)

estimated variance-covariance matrix of the weights

**scores_**float

if computed, value of the objective function (to be maximized)

**n_iter_**int

The actual number of iterations to reach the stopping criterion.

Added in version 1.3.

**intercept_**float

Independent term in decision function. Set to 0.0 iffit_intercept = False.

**X_offset_**float

If fit_intercept=True, offset subtracted for centering data to a zero mean. Set to np.zeros(n_features) otherwise.

**X_scale_**float

Set to np.ones(n_features).

**n_features_in_**int

Number of features seen during fit.

Added in version 0.24.

**feature_names_in_**ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when Xhas feature names that are all strings.

Added in version 1.0.

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=15Their 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.])

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 andn_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_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

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_fittedis 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) w.r.t. y.

Notes

The \(R^2\) score used when calling score on a regressor usesmultioutput='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 forMultiOutputRegressor).

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.

set_predict_request(*, return_std: bool | None | str = '$UNCHANGED$') → ARDRegression[source]#

Request metadata passed to the predict method.

Note that this method is only relevant ifenable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside aPipeline. Otherwise it has no effect.

Parameters:

return_stdstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for return_std parameter in predict.

Returns:

selfobject

The updated object.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ARDRegression[source]#

Request metadata passed to the score method.

Note that this method is only relevant ifenable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside aPipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in score.

Returns:

selfobject

The updated object.