Joint inverse covariances estimation with mutual linear structure

We consider the problem of joint estimation of structured inverse covariance matrices. We assume the structure is unknown and perform the estimation using groups of measurements coming from populations with different covariances. Given that the inverse covariances span a low dimensional affine 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 exploring the underlying structure and provide its efficient implementation. Numerical simulations are presented to illustrate the performance benefits of the proposed algorithm.