Separable Geodesic Lagrangian Monte Carlo for Inference in 2-Way Covariance Models

TL;DR

This paper introduces a novel geodesic Hamiltonian Monte Carlo method tailored for efficient inference in matrix normal models with Kronecker-structured covariance, leveraging the geometry of the parameter space.

Contribution

It develops a new sampler based on the pullback geometry of Kronecker-structured covariance matrices, extending MCMC techniques beyond Gibbs sampling for these models.

Findings

Efficient sampling in matrix normal models with Kronecker covariance.

Improved mixing and convergence over traditional methods.

Novel geometric approach for MCMC in structured covariance models.

Abstract

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the vector normal, also known as separable covariance matrices. Separable covariance matrices have been studied extensively in the context of multiway data, but little work has been done within the scope of MCMC beyond Gibbs sampling. This paper aims to fill this gap by considering the pullback geometry induced from the Kronecker structure of the parameter space to develop a geodesic Hamiltonian Monte Carlo sampler.