Bayesian generalized fused lasso modeling via NEG distribution

TL;DR

This paper introduces a Bayesian generalized fused lasso model using the NEG prior, enhancing sparsity control and model flexibility, with demonstrated superior performance over traditional fused lasso methods.

Contribution

It proposes a novel Bayesian fused lasso approach with NEG prior for more flexible regularization and an exact sparse solution algorithm.

Findings

Superior performance in simulations and real data analyses

More versatile sparse modeling than ordinary fused lasso

Effective construction of exact sparse solutions

Abstract

The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed into the difference of successive regression coefficients. The proposed method enables us to construct a more versatile sparse model than the ordinary fused lasso by using a flexible regularization term. We also propose a sparse fused algorithm to produce exact sparse solutions. Simulation studies and real data analyses show that the proposed method has superior performance to the ordinary fused lasso.