Asymptotic Matrix Variate von-Mises Fisher and Bingham Distributions with Applications

TL;DR

This paper derives simple asymptotic approximations for the normalization constants of matrix variate von-Mises Fisher and Bingham distributions, enabling more efficient sampling in practical applications.

Contribution

It introduces novel asymptotic formulas for normalization constants using random matrix theory, improving computational efficiency in statistical modeling on Stiefel manifolds.

Findings

Approximate normalization constants are accurate in practical regimes.

Sampling complexity is significantly reduced using the new approximations.

The methods facilitate applications in signal processing and related fields.

Abstract

Probability distributions in Stiefel manifold such as the von-Mises Fisher and Bingham distributions find diverse applications in signal processing and other applied sciences. Use of these statistical models in practice is complicated by the difficulties in numerical evaluation of their normalization constants. In this letter, we derive asymptotical approximations to the normalization constants via recent results in random matrix theory. The derived approximations take simple forms and are reasonably accurate in regimes of practical interest. As an application, we show that the proposed analytical results lead to a remarkably reduction of the sampling complexity compared to existing simulation based approaches.