Kronecker-structured Covariance Models for Multiway Data

TL;DR

This paper reviews tensor-based covariance models for high-dimensional multiway data, emphasizing their application in multichannel signal processing and space weather prediction, highlighting recent progress and inference techniques.

Contribution

It provides a comprehensive review of tensor-valued covariance models and their inference methods for high-dimensional multiway data, with a focus on recent developments.

Findings

Tensor models effectively capture multiway data covariance structures.

Application to space weather prediction demonstrates practical utility.

Advances in inference methods improve model estimation accuracy.

Abstract

Many applications produce multiway data of exceedingly high dimension. Modeling such multi-way data is important in multichannel signal and video processing where sensors produce multi-indexed data, e.g. over spatial, frequency, and temporal dimensions. We will address the challenges of covariance representation of multiway data and review some of the progress in statistical modeling of multiway covariance over the past two decades, focusing on tensor-valued covariance models and their inference. We will illustrate through a space weather application: predicting the evolution of solar active regions over time.