bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression¶

class bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression(n_iter=300, tol=0.001, optimizer='fp', fit_intercept=True, normalize=True, perfect_fit_tol=1e-06, alpha=1, copy_X=True, verbose=False)¶

Bases: BayesianLinearRegression

Bayesian Regression with type II maximum likelihood (Empirical Bayes)

Parameters:¶

n_iter: int, optional (DEFAULT = 300): Maximum number of iterations
tol: float, optional (DEFAULT = 1e-3): Threshold for convergence
optimizer: str, optional (DEFAULT = ‘fp’): Method for optimization , either Expectation Maximization or Fixed Point Gull-MacKay {‘em’,’fp’}. Fixed point iterations are faster, but can be numerically unstable (especially in case of near perfect fit).
fit_intercept: bool, optional (DEFAULT = True): If True includes bias term in model
perfect_fit_tol: float (DEAFAULT = 1e-5): Prevents overflow of precision parameters (this is smallest value RSS can have). ( !!! Note if using EM instead of fixed-point, try smaller values of perfect_fit_tol, for better estimates of variance of predictive distribution )
alpha: float (DEFAULT = 1): Initial value of precision paramter for coefficients ( by default we define very broad distribution )
copy_Xboolean, optional (DEFAULT = True): If True, X will be copied, otherwise will be
verbose: bool, optional (Default = False): If True at each iteration progress report is printed out

Attributes¶

coef_array, shape = (n_features): Coefficients of the regression model (mean of posterior distribution)
intercept_: float: Value of bias term (if fit_intercept is False, then intercept_ = 0)
alpha_float: Estimated precision of coefficients
beta_float: Estimated precision of noise
eigvals_array, shape = (n_features, ): Eigenvalues of covariance matrix (from posterior distribution of weights)
eigvecs_array, shape = (n_features, n_featues): Eigenvectors of covariance matrix (from posterior distribution of weights)

__init__(n_iter=300, tol=0.001, optimizer='fp', fit_intercept=True, normalize=True, perfect_fit_tol=1e-06, alpha=1, copy_X=True, verbose=False)¶

Methods

`__init__`([n_iter, tol, optimizer, ...])
`fit`(X, y)	Fits Bayesian Linear Regression using Empirical Bayes
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X[, return_std])	Computes predictive distribution for test set.
`predict_dist`(X)	Calculates mean and variance of predictive distribution for each data point of test set.(Note predictive distribution for each data point is Gaussian, therefore it is uniquely determined by mean and variance)
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.
`set_predict_request`(*[, return_std])	Request metadata passed to the `predict` method.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

fit(X, y)¶

Fits Bayesian Linear Regression using Empirical Bayes

Parameters¶

X: array-like of size [n_samples,n_features]: Matrix of explanatory variables (should not include bias term)
y: array-like of size [n_features]: Vector of dependent variables.

Returns¶

object: self: self

get_metadata_routing()¶

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)¶

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)¶

Computes predictive distribution for test set. Predictive distribution for each data point is one dimensional Gaussian and therefore is characterised by mean and variance.

Parameters¶

X: {array-like, sparse} (n_samples_test, n_features): Test data, matrix of explanatory variables

Returns¶

: list of length two [y_hat, var_hat]

y_hat: numpy array of size (n_samples_test,)
Estimated values of targets on test set (i.e. mean of predictive distribution)

var_hat: numpy array of size (n_samples_test,)
Variance of predictive distribution

predict_dist(X)¶

Calculates mean and variance of predictive distribution for each data point of test set.(Note predictive distribution for each data point is Gaussian, therefore it is uniquely determined by mean and variance)

Parameters¶

x: array-like of size (n_test_samples, n_features): Set of features for which corresponding responses should be predicted

Returns¶

:list of two numpy arrays [mu_pred, var_pred]

mu_prednumpy array of size (n_test_samples,)
Mean of predictive distribution

var_pred: numpy array of size (n_test_samples,)
Variance of predictive distribution

score(X, y, sample_weight=None)¶

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) w.r.t. 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)¶

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 = '$UNCHANGED$') → EBLinearRegression¶

Request metadata passed to the predict method.

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

The options for each parameter are:

True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to predict.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

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 a Pipeline. 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 = '$UNCHANGED$') → EBLinearRegression¶

Request metadata passed to the score method.

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

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

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 a Pipeline. 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.