bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace¶

class bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace(n_iter=1000, n_Kfold=10, tol=1e-07, fit_intercept=False, bias_term=True, copy_X=True, verbose=False)¶

Bases: object

Sparse regression with Bayesian Compressive Sensing as described in Alg. 1 (Fast Laplace) of Ref.[1], which updated formulas from [2].

sigma2: noise precision (sigma^2) nu fixed to 0

uqlab/lib/uq_regression/BCS/uq_bsc.m

Parameters¶

n_iter: int, optional (DEFAULT = 1000): Maximum number of iterations
tol: float, optional (DEFAULT = 1e-7): If absolute change in precision parameter for weights is below threshold algorithm terminates.
fit_interceptboolean, optional (DEFAULT = True): whether 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).
copy_Xboolean, optional (DEFAULT = True): If True, X will be copied; else, it may be overwritten.
verboseboolean, optional (DEFAULT = FALSE): Verbose mode when fitting the model

Attributes¶

coef_array, shape = (n_features): Coefficients of the regression model (mean of posterior distribution)
alpha_float: estimated precision of the noise
active_array, dtype = np.bool, shape = (n_features): True for non-zero coefficients, False otherwise
lambda_array, shape = (n_features): estimated precisions of the coefficients
sigma_array, shape = (n_features, n_features): estimated covariance matrix of the weights, computed only for non-zero coefficients

References¶

[1] Babacan, S. D., Molina, R., & Katsaggelos, A. K. (2009). Bayesian: compressive sensing using Laplace priors. IEEE Transactions on image processing, 19(1), 53-63.
[2] Fast marginal likelihood maximisation for sparse Bayesian models: (Tipping & Faul 2003). (http://www.miketipping.com/papers/met-fastsbl.pdf)

__init__(n_iter=1000, n_Kfold=10, tol=1e-07, fit_intercept=False, bias_term=True, copy_X=True, verbose=False)¶

Methods

`__init__`([n_iter, n_Kfold, tol, ...])
`fit`(X, y)
`fit_`(X, y, sigma2)
`predict`(X[, return_std])	Computes predictive distribution for test set.

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 based on Ref.[1] Section 3.3.2.

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

References¶

[1] Bishop, C. M. (2006). Pattern recognition and machine learning. springer.