A Bayesian Framework for Regularized Estimation in Multivariate Models Integrating Approximate Computing Concepts

Abstract

This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding (quantization), thereby connecting two distinct paradigms: Bayesian inference and approximate computing. Next, Bayesian estimation of the means from two independent multivariate normal samples is employed to justify shrinkage estimators, i.e., means shrunk toward the pooled mean. Finally, regularized linear discriminant analysis (LDA) is considered. Various shrinkage strategies for the mean are justified from a Bayesian perspective, and novel algorithms for their computation are proposed. The proposed methods are illustrated by numerical experiments on real and simulated data.