Approximate Algorithm for Horseshoe Prior

Provides exact and approximate algorithms for the horseshoe prior in linear regression models, which were proposed by Johndrow et al. (2020) < https://www.jmlr.org/papers/v21/19-536.html>.

Mhorseshoe

Overview

Mhorseshoe is a package for a high-dimensional Bayesian linear modeling algorithm using a horseshoe prior. A feature of this package is that it implements approximate MCMC algorithm from Johndrow et al. (2020) and provides a horseshoe estimator that can effectively reduce computational costs for high-dimensional sparse data. This package provides two different algorithm functions :

-exact_horseshoe() Run the horseshoe estimator.

-approx_horseshoe() Run the horseshoe estimator with the approximate algorithm applied.

Installation

install.package("Mhorseshoe")

Usage

The following linear model assumptions are made.

$$L(y\ |\ x, \beta, \sigma^2) = (\frac{1}{\sqrt{2\pi}\sigma})^{-N/2}exp { -\frac{1}{2\sigma^2}(y-X\beta)^T(y-X\beta)},\ X \in \mathbb{R}^{N \times p},\ y \in \mathbb{R}^{N},\ \beta \in \mathbb{R}^{p}$$

• $X \in \mathbb{R}^{N \times p}$ : Matrix of covariates.
• $y \in \mathbb{R}^{N}$ : Response variable.

# Run functions from the Mhorseshoe package
ex_result <- exact_horseshoe(y, X, burn = 5000, iter = 10000)
ap_result <- approx_horseshoe(y, X, burn = 5000, iter = 10000)

# posterior mean of beta
ex_betahat <- ex_result$BetaHat
ap_betahat <- ap_result$BetaHat

# 95% posterior credible intervals
ex_LeftCI <- ex_result$LeftCI
ex_RightCI <- ex_result$RightCI
ap_LeftCI <- ap_result$LeftCI
ap_RightCI <- ap_result$RightCI

References

Johndrow, J., Orenstein, P., & Bhattacharya, A. (2020). Scalable Approximate MCMC Algorithms for the Horseshoe Prior. In Journal of Machine Learning Research (Vol. 21).

If you would like to discuss this package, please email leehuimin115@g.skku.edu