Joint Covariance Estimation with Mutual Linear Structure

TL;DR

This paper introduces a novel method for jointly estimating multiple structured covariance matrices from heterogeneous data sets by uncovering their mutual low-dimensional affine structure using PCA, leading to improved estimation accuracy.

Contribution

The paper proposes an efficient PCA-based algorithm to discover the shared structure among covariance matrices and enhance their estimation from diverse training data.

Findings

The algorithm effectively uncovers the mutual structure in covariance matrices.

Performance bounds are derived and validated through simulations.

The method outperforms existing approaches in structured covariance estimation.

Abstract

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method.