Anti-correlation-Gaussian

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

Files

• SourceCode.R — l1ball.linreg(X, y, ...): a blocked Gibbs sampler for the L1-ball-prior linear regression model that uses the anti-correlation Gaussian data-augmentation step described in the paper.
• SliceSampler.R — scalar and directional slice samplers (Neal, Slice Sampling, 2003). Used by l1ball.linreg to update κ; can be sourced standalone.
• LinearReg.R — toy variable-selection demo (n = 300, p = 500) that produces estimation, trace, and ACF plots.
• TruncatedMVN.R — truncMVN(...): extension of the anti-correlation trick to sampling a multivariate normal truncated to a box, plus a 2-D demo.
• tests/test_samplers.R — self-contained smoke + correctness tests (see Testing).
• 100206_tfMRI_MOTOR_LR.nii.gz — Git-LFS pointer for the fMRI dataset used in the paper. Requires git lfs install and git lfs pull to fetch the actual file.

Dependencies

Required:

• R ≥ 4.0
• truncnorm

Optional (only if you run the corresponding feature/demo):

• BoomSpikeSlab  — init_method = "SSVS" in l1ball.linreg
• tmvtnorm, mvtnorm, dplyr, tidyr, tibble, ggplot2, gridExtra  — TruncatedMVN.R demo
• ggplot2  — LinearReg.R demo

Install in R:

install.packages(c("truncnorm", "ggplot2"))
# Optional extras:
install.packages(c("BoomSpikeSlab", "tmvtnorm", "mvtnorm",
                   "dplyr", "tidyr", "tibble", "gridExtra"))

Quick start

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, run

Rscript LinearReg.R

Testing

A small test script is provided that

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

Run from the repo root:

Rscript tests/test_samplers.R

Notes on the fMRI data

100206_tfMRI_MOTOR_LR.nii.gz is tracked with Git LFS. After cloning, run

git lfs install
git lfs pull

to download the binary. None of the R scripts in this repository load it directly; it is included for reproducibility of the paper's fMRI experiments.

License

MIT.