Anti-correlation Gaussian Data Augmentation

Open-source · github.com/YuZh98/Anti-correlation-Gaussian

Code accompanying the paper Gibbs Sampling using Anti-correlation Gaussian Data Augmentation, with Applications to L1-ball-type Models.

Files

File	Purpose
`SourceCode.R`	`l1ball.linreg(X, y, ...)`: blocked Gibbs sampler for the L1-ball-prior linear regression model using the anti-correlation Gaussian data-augmentation step
`SliceSampler.R`	Scalar and directional slice samplers (Neal, 2003). Used to update κ; can be sourced standalone
`LinearReg.R`	Toy variable-selection demo (`n = 300`, `p = 500`) producing estimation, trace, and ACF plots
`TruncatedMVN.R`	Extension of the anti-correlation trick to sampling a multivariate normal truncated to a box, plus a 2-D demo
`tests/test_samplers.R`	Smoke + correctness tests

Quick start

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source("SliceSampler.R")
source("SourceCode.R")

set.seed(1)
n <- 100; p <- 20
X <- matrix(rnorm(n * p), n, p)
beta_true <- c(rep(2, 5), rep(0, p - 5))
y <- as.numeric(X %*% beta_true + rnorm(n))

fit <- l1ball.linreg(X, y, steps = 4000, burnin = 2000, thin = 1,
                     init_method = "random", verbose = FALSE)
round(fit$theta.est, 2)

To reproduce the paper’s linear-regression figures:

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Rscript LinearReg.R

Testing

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Rscript tests/test_samplers.R

Checks that truncMVN reproduces the moments of a known truncated MVN, and that l1ball.linreg recovers the support and signs of the true coefficients on a small synthetic problem.