Empirical Bayesian Elastic Net (EBEN) for Generalized Linear Models

We provide extremely efficient procedures for fitting the empirical Bayesian methods with lasso and elastic net hierarchical priors for linear regression (gaussian), and logistic regression (binomial) models. EBEN is a sister package to EBglmnet (available in CRAN). Both packages share key features include:

• sparse variable selection and effect estimation via generalized linear regression models;
• high dimensionality with p>>n; and
• significance test (with output of p-value) for nonzero effects; and
• closed-form solution for Bayesian variance estimation in an iterative cooridinate descent algorithm estimating the Bayesian means.

The implementation enables extremely efficient computation comparable with that of glmnet package.

When you need EBEN

While EBglmnet offers generic functions for a broad range of use cases, EBEN takes care of the following special cases:

• two-way interaction terms (epistasis) are included with epis = TRUE: for input independent parameter X with n x p dimension, the functions will evaluate p(p-1)/2 additional parameters;
• group Empirical Bayesian Lasso are avaiable with group = TRUE: the penalty parameter for the group of p(p-1)/2 parameters are weighted with group size in comparing with the group origin p variables.

Further readings

Details may be found in Huang A. and Liu D (2016), Huang A., Xu S., and Cai X. (2015), Huang A. (2014), Huang A., Xu S., and Cai X. (2013), and Cai X., Huang A., and Xu S., (2011).

Version notes

Version 5.1 is a major release with several new features, including:

• group Empirical Bayesian Lasso (EBlasso) and built-in two-way interaction support moved to EBEN package.
• BLAS/Lapack routines are updated according to R-API change.

References