The EB Elastic Net Algorithm for Gaussian Model

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Description

General linear regression, normal-Gamma (NG) hierarchical prior for regression coefficients

Usage

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EBelasticNet.Gaussian(BASIS, Target, lambda, alpha,Epis = "no",verbose = 0)

Arguments

BASIS

sample matrix; rows correspond to samples, columns correspond to features

Target

Response each individual

lambda

Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; lambda>0

alpha

Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; 0<alpha<1

Epis

"yes" or "no" for including two-way interactions

verbose

0 or 1; 1: display message; 0 no message

Details

If Epis="yes", the program adds two-way interaction of K*(K-1)/2 more columns to BASIS

Value

weight

the none-zero regression coefficients:
col1,col2 are the indices of the bases(main if equal);
col3: coefficent value;
col4: posterior variance;
col5: t-value;
col6: p-value

WaldScore

Wald Score

Intercept

Intercept

lambda

the hyperparameter; same as input lambda

alpha

the hyperparameter; same as input alpha

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79

Examples

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library(EBEN)
data(BASIS)
data(y)
n = 50;
k = 100;
BASIS = BASIS[1:n,1:k];
y  = y[1:n];
Blup = EBelasticNet.Gaussian(BASIS, y,lambda = 0.0072,alpha = 0.95, Epis = "no",verbose = 0)
betas 			= Blup$weight
betas