Bayesian factorization via $L_{1/2}$ shrinkage

2026-03-28

AI Summary

This work addresses the computational challenges in existing Bayesian factor models arising from the complex hierarchical structure of ordered shrinkage priors, which hinder efficient posterior inference. To overcome this limitation, we propose a novel Bayesian factorization method based on an $L_{1/2}$ shrinkage prior that preserves the desirable ordered shrinkage property of factor loadings while substantially simplifying the prior architecture. The resulting model admits both exact Gibbs sampling and an efficient variational approximation, achieving a favorable balance between computational efficiency and inferential accuracy. Extensive numerical experiments demonstrate that the proposed approach consistently outperforms state-of-the-art Bayesian factor models in terms of both estimation precision and computational speed.

Abstract

Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index increases. However, existing increasing shrinkage priors often possess complex hierarchical structures that complicate posterior inference. To address this issue, we propose using an $L_{1/2}$ shrinkage prior. We demonstrate that by carefully setting the parameters in the hyper prior of its global shrinkage parameters, the increasing shrinkage property is preserved. Our prior specification is simple, facilitating the construction of an efficient Gibbs sampler for exact posterior inference. For faster computation, we also propose a variational approximation algorithm. Through numerical studies, we compare our approaches with current popular Bayesian methods for factor models, demonstrating their merits in terms of accuracy and computational efficiency.

Problem

• Bayesian factor models
• increasing shrinkage priors
• posterior inference
• hierarchical structure
• factor loadings

Innovation

• L_{1/2} shrinkage
• Bayesian factor models
• increasing shrinkage prior
• Gibbs sampler
• variational approximation