HDBRR: High Dimensional Bayesian Ridge Regression without MCMC.

In HDBRR: High Dimensional Bayesian Ridge Regression without MCMC

High Dimensional Bayesian Ridge Regression without MCMC.

Description

Ridge regression provide biased estimators of the regression parameters with lower variance. The HDBRR ("High Dimensional Bayesian Ridge Regression") function fits Bayesian Ridge regression without MCMC, this one uses the SVD or QR decomposition for the posterior computation.

Usage

HDBRR(y, X, n0 = 5, p0 = 5, s20 = NULL, d20 = NULL, h = 0.5,
    intercept = TRUE, vpapp = TRUE,npts = NULL,c = NULL,
    corpred = NULL, method = c("svd","qr"),bigmat = TRUE, ncores = 2, svdx = NULL)

Arguments

y	The data vector (numeric, n) NAs allowed.
X	Design Matrix of dimension n x p.
n0, p0	n0/2 and p0/2 are the shape parameter of the Gamma Inverse prior assigned to the residual variance and the shape parameter of the Gamma Inverse prior assigned to the Beta's variance respectively. The default value for n0/2 and p0/2 parameter is 5.
s20, d20	(n0s20)/2 and (p0d20)/2 are the scale parameter of the Gamma Inverse prior assigned to the residual variance and the scale parameter of the Gamma Inverse prior assigned to the Beta's variance respectively. The default value for the s20 and d20 is NULL. If the scale is not specified a value is calculated with h and quantiles.
h	(numeric, 0<h<1) shrinkage factor. Only used if the hyper-parameters are not specified; If h -> 0 then we have greater shrinkage, this is, \beta -> 0. If h -> 1 then we have less shrinkage.
intercept	Logic value. The default value for the intercept is TRUE.
vpapp	Logic value. Compute an approximation of the predictive variance. The default value for the vpapp is TRUE.
npts	Number (integer) of points used to evaluate the u's density for the numeric aprroach. The default value for the npts parameter is 200.
c	ratio of Gaussian densities (Spike/Slab) in the prior mixture density of each Beta for variable selection.
corpred	The method for the compute of the correlation, there are two methods, Empirical Bayes ("eb") and Bayesian ("b") method. The default value for the parameter corpred is NULL. If the values is NULL then the corr and edf values will be NULL.
method	Options for the posterior computation. There are two methods available: "qr" decomposition of X*t(X) and "svd" decomposition of matrix X. The default value for the method is SVD decomposition.
bigmat	Use of the bigstatsr package. The default value for bigmat is TRUE.
ncores	Number of the cores for computation. The default value for the ncores is 2, you can detect your number of cores with detectCores() and use it (iOS and Linux).
svdx	It is possible to add the svd. The default value es NULL.

Details

Ridge regression is a useful tool to deal with collinearity in the homoscedastic linear regression model providing biased estimators of the regression parameters with lower variance than the least square estimators. The model

y = X\beta + \epsilon

where \epsilon vector is assumed Normal with mean vector 0 and covariance matrix \sigma^2 I_n. For further details see the vignettes in the package.

Value

List containing the following components:

betahat	Vector (numeric, p) with the betas estimates.
yhat	Vector (numeric, n) with the y's estimates.
sdyhat	Vector (numeric, n) with the standard deviation of the predicts values.
sdpred	Vector (numeric, n) with the standard deviation of predict variances.
varb	Vector (numeric, p) with the beta's variance.
sigsqhat	Value (numeric) of the residual variance estimate.
sigbsqhat	Value (numeric) of the Beta's variance estimate.
u	Vector (numeric, npts) with the u's values.
postu	Vector (numeric, npts) with the values of the u posterior.
uhat	Value (numeric) of u estimated.
umode	Value (numeric) of the posterior mode of u.
whichNa	Value (integer) of NAs in the y vector.
phat	Vector (numeric, p), selection probability of x_i.
delta	Used in the variable selection.
edf	Value (numeric) of the effective degrees of freedom for regression.
corr	Vector (numeric, n) of the correlation between y_i estimates and y_i.
svdx	The svd decomposition.

Author(s)

Sergio Perez-Elizalde, Blanca E. Monroy-Castillo, Paulino Perez-Rodriguez, Jose Crossa.

Examples

## Not run: 

set.seed(123)
n <- 50
p <- 10
X <- matrix(rnorm(n * p), n, p)
y <- 1 + X[, 1] - 0.5 * X[, 2] + rnorm(n)
fitall <- HDBRR(y, X, intercept = TRUE, corpred = "eb", c = 100)
fitall
summary(fitall, crit = 0)
plot(fitall, crit = 0)
predict(fitall)


## End(Not run)

HDBRR documentation built on Sept. 23, 2026, 5:07 p.m.