Bayesian Fused Lasso Modeling via Horseshoe Prior

TL;DR

This paper introduces a Bayesian fused lasso approach using horseshoe priors to improve shrinkage of regression coefficients and their differences, enhancing performance over existing methods.

Contribution

It proposes a novel Bayesian fused lasso model with horseshoe priors on differences, preventing over-shrinkage and improving estimation accuracy.

Findings

Outperforms existing methods in simulations

Demonstrates effectiveness on real data

Prevents over-shrinkage of coefficient differences

Abstract

Bayesian fused lasso is one of the sparse Bayesian methods, which shrinks both regression coefficients and their successive differences simultaneously. In this paper, we propose a Bayesian fused lasso modeling via horseshoe prior. By assuming a horseshoe prior on the difference of successive regression coefficients, the proposed method enables us to prevent over-shrinkage of those differences. We also propose a Bayesian hexagonal operator for regression with shrinkage and equality selection (HORSES) with horseshoe prior, which imposes priors on all combinations of differences of regression coefficients. Simulation studies and an application to real data show that the proposed method gives better performance than existing methods.