Near optimal sample complexity for matrix and tensor normal models via geodesic convexity
The matrix normal model, that is, the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower-dimensional factors, is frequently used to model matrix-variate data. The tensor normal model generalizes this family to Kronecker products of three or more factors. We study the estimation of the Kronecker factors of the covariance matrix in the matrix and tensor normal models. For the above models, we show that the maximum…