Hierarchical sparsity priors for regression models

TL;DR

This paper introduces hierarchical sparsity priors for regression models that promote related shrinkage of coefficients, improving modeling in high-dimensional settings with structured variable effects.

Contribution

It proposes a novel hierarchical prior framework that captures dependencies among regression coefficients, enhancing sparse regression modeling with structured effects.

Findings

Priors encourage related coefficients to shrink towards zero together.

Applications to linear models with interactions demonstrate improved variable selection.

Framework encompasses heredity principles for interaction effects.

Abstract

We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions when the effects are considered related. These priors allow dependence between the regression coefficients and encourage related shrinkage towards zero of different regression coefficients. The properties of these priors are discussed and applications to linear models with interactions and generalized additive models are used as illustrations. Ideas of heredity relating different levels of interaction are encompassed.