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)
Read more in the User Guide.
- Parameters
- n_iterint, default=300
Maximum number of iterations.
- 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).
- normalizebool, default=False
This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
.Deprecated since version 1.0:
normalize
was deprecated in version 1.0 and will be removed in 1.2.- 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)
- intercept_float
Independent term in decision function. Set to 0.0 if
fit_intercept = False
.- X_offset_float
If
normalize=True
, offset subtracted for centering data to a zero mean.- X_scale_float
If
normalize=True
, parameter used to scale data to a unit standard deviation.- n_features_in_int
Number of features seen during fit.
New in version 0.24.
- feature_names_in_ndarray of shape (
n_features_in_
,) Names of features seen during fit. Defined only when
X
has feature names that are all strings.New in version 1.0.
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 ourself.lambda_
ARD is a little different than the slide: only dimensions/features for whichself.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 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_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 ofy
, 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)
, wheren_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 usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
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.