Joint Inverse Covariances Estimation with Mutual Linear Structure

TL;DR

This paper introduces a novel method for jointly estimating multiple structured inverse covariance matrices by exploiting their low-dimensional linear subspace, leading to improved estimation accuracy.

Contribution

The paper proposes a new optimization algorithm that discovers and leverages the linear structure among inverse covariances for better estimation performance.

Findings

The algorithm effectively identifies the underlying linear subspace.

Numerical simulations show improved estimation accuracy.

The method outperforms existing approaches in structured inverse covariance estimation.

Abstract

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim is to determine this structure. It is then utilized to improve the estimation of the inverse covariances. We propose a novel optimization algorithm discovering and exploiting the underlying structure and provide its efficient implementation. Numerical simulations are presented to illustrate the performance benefits of the proposed algorithm.