Selection of tuning parameters in bridge regression models via Bayesian information criterion

TL;DR

This paper introduces a Bayesian information criterion for selecting tuning parameters in bridge regression models, improving model selection for sparse and non-sparse linear regressions.

Contribution

The paper proposes a novel Bayesian-based model selection criterion specifically designed for tuning parameter selection in bridge regression models.

Findings

The criterion effectively selects optimal tuning parameters in numerical experiments.

It improves model sparsity and prediction accuracy.

The method is applicable to both sparse and non-sparse models.

Abstract

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.