Joint Inverse Covariances Estimation with Mutual Linear Structure
This work addresses a domain-specific problem in statistical estimation for groups of measurements with different covariances, presenting an incremental improvement through a new algorithm.
The paper tackles the problem of jointly estimating structured inverse covariance matrices by assuming they span a low-dimensional linear subspace, and proposes a novel optimization algorithm that discovers and exploits this structure to improve estimation, with numerical simulations demonstrating performance benefits.
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.