🤖 AI Summary
This paper addresses computational and modeling bottlenecks in Bayesian regularization for multivariate statistical models. Methodologically, it introduces a unified Bayesian framework integrating parameter quantization (rounding) and approximate inference: shrinkage estimators—such as those shrinking toward a common mean—are rigorously interpreted as posterior means under specific priors, and an efficient approximate Bayesian algorithm is developed to balance accuracy and scalability. Theoretically, it establishes a rigorous connection between Bayesian inference and numerical approximation, providing the first unified Bayesian interpretation of classical shrinkage strategies. Applicationally, the framework is extended to regularized Linear Discriminant Analysis (LDA), yielding substantial improvements in classification stability and parameter estimation accuracy on both synthetic and real-world datasets. The approach thus bridges theoretical rigor with practical efficiency in high-dimensional multivariate inference.
📝 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.