SBLassoRSq: R-square-Safe-Bayesian Lasso

In SafeBayes: Generalized and Safe-Bayesian Ridge and Lasso Regression

Description

The function SBLassoRSq (R-square-Safe-Bayesian Lasso) provides a Gibbs sampler together with the R-square-Safe-Bayesian algorithm for Bayesian lasso regression models with fixed variance.

Usage

SBLassoRSq(y, X = NULL, sigma2 = NULL, etaseq = 1, prior = NULL, nIter = 1100, 
	burnIn = 100, thin = 10, minAbsBeta = 1e-09, pIter = TRUE)

Arguments

y	Vector of outcome variables, numeric, NA allowed, length n.
X	Design matrix, numeric, dimension n x p, n >= 2.
sigma2	Fixed variance parameter sigma^2, numeric. Default NULL, in which case the variance will be estimated from the data per addition of new data point in the Safe-Bayesian algorithm.
etaseq	Vector of learning rates eta, numeric, 0 <= eta <= 1. Default 1.
prior	List containing the following elements prior$varE: prior for the variance parameter σ^2 with parameters $df and $S for respectively degrees of freedom and scale parameters for an inverse-chi-square distribution. Default (0,0). prior$lambda: prior for the penalty parameter lambda with three items. $value Initial value for lambda. Default 50 $type Can be ‘fixed’: initial value is used as fixed penalty parameter or ‘random’, in which case a prior for lambda is specified. Default ‘random’. For a Gamma prior on lambda^2: $shape for shape parameter and $rate for the rate parameter; for a Beta prior on lambda: $shape1, $shape2 and $max for lambda proportional to Beta(lambda/max, shape1, shape2). Default: Gamma(0,0).
nIter	Number of iterations, integer. Default 1100.
burnIn	Number of iterations for burn-in, integer. Default 100.
thin	Number of iterations for thinning, integer. Default 10.
minAbsBeta	Minimum absolute value of sampled coefficients beta to avoid numerical problems, numeric. Default 10^-9.
pIter	Print iterations, logical. Default TRUE.

Details

Details on the Safe-Bayesian lasso can be found in Chapter 2 of (de Heide, 2016). The implementation of the Gibbs sampler is based on the BLR package of (de los Campos et al., 2009).

The Safe-Bayesian algorithm was proposed by Grunwald (2012) as a method to learn the learning rate for the generalized posterior to deal with model misspecification.

Value

$y	Vector of original outcome variables.
$mu	Posterior mean of the intercept.
$varE	Posterior mean of of the variance.
$yHat	Posterior mean of mu + X*beta + epsilon.
$SD.yHat	Corresponding standard deviation.
$whichNa	Vector with indices of missing values of y.
$fit$pD	Estimated number of effective parameters.
$fit$DIC	Deviance Information Criterion.
$lambda	Posterior mean of lambda.
$bL	Posterior mean of beta.
$SD.bL	Corresponding standard deviation.
$tau2	Posterior mean of tau^2.
$prior	List containing the priors used.
$nIter	Number of iterations.
$burnIn	Number of iterations for burn-in.
$thin	Number of iterations for thinning.
$CMRSEallen	List of cumulative posterior-expected posterior-randomized square-loss per eta.
$eta.min	Learning rate eta minimizing the cumulative posterior-expected posterior-randomized square-loss.

Author(s)

R. de Heide

References

de Heide, R. 2016. The Safe-Bayesian Lasso. Master Thesis, Leiden University.

de los Campos G., H. Naya, D. Gianola, J. Crossa, A. Legarra, E. Manfredi, K. Weigel and J. Cotes. 2009. Predicting Quantitative Traits with Regression Models for Dense Molecular Markers and Pedigree. Genetics 182: 375-385.

Grunwald, P.D. 2012. chapter The Safe Bayesian. Algorithmic Learning Theory: 23rd International Conference, ALT 2012, Lyon, France, October 29-31, 2012. Proceedings. 169-183. Springer Berlin Heidelberg

Examples

rm(list=ls())
# Simulate data
x <- runif(10, -1, 1) # 10 random uniform x's between -1 and 1
y <- NULL

# for each x, an y that is 0 + Gaussian noise
for (i in 1:10) {
  y[i] <-  0 + rnorm(1, mean=0, sd=1/4) 
  }

plot(x,y)

## Not run: 
# Let R-square-SafeBayes learn the learning rate 
sbobj <- SBLassoRSq(y, x, etaseq=c(1, 0.5, 0.25))

# eta 
sbobj$eta.min
## End(Not run)

SafeBayes documentation built on May 1, 2019, 9:23 p.m.