Pairwise Fusion Approach Incorporating Prior Constraint Information

Abstract

In this paper, we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information. The sparsity means that a small fraction of regression coefficients is nonzero, and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group. A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints. We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence. The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information. Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.

Keywords

Alternating direction method of multipliers / Prior constraint information / Sparsity / Homogeneity / Linear regression