Empirical Bayesian Modeling of Kronecker Product Relevancy in Gaussian Arrays

Time: 4:30-5:30 p.m.
Date: Wednesday, October 15, 2025
Speaker: Quinn Simonis, Visiting Assistant Professor of Statistics, Cornell University
Title: Empirical Bayesian Modeling of Kronecker Product Relevancy in Gaussian Arrays
 

Abstract: Bayesian inference of large covariances has become increasingly difficult with the growing size and often large time complexity of covariance estimation techniques. For observations which admit a multiway structure, the tensor normal likelihood has become ubiquitous due to its form giving a mode wise parameterization of the covariance. This representation of the covariance allows for modeling the covariance through small sequential mode-wise operations. While computationally convenient, the resulting covariance imposes a strict unrealistic structure.
As a means to alleviate the structural assumptions imposed by the tensor normal's covariance, we consider parameterizing the Cholesky factor of the precision matrix of a multivariate normal through an SVD like Kronecker Product expansion. This parameterization directly relaxes one of the structural assumptions of the tensor normal distribution's covariance without loss of analytic tractability of the likelihood. We connect this parametrization with the Log-Cholesky Riemannian metric's Frechet Mean, and use this parametrization to then construct a hierarchical empirical Bayes model for relevancy detection under the sum of Kronecker products representation. 

Bio: Quinn Simonis is a Visiting Assistant Professor of Statistics at Cornell University. He earned his PhD in Statistics from Cornell in 2025 under the supervision of Professors Martin Wells and David Matteson. His research interests broadly include statistical methods for inference on Riemannian manifold distributed parameters and machine learning methods for manifold distributed data.