The geometry of Gaussian double Markovian distributions

Abstract

Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the matrix and its inverse.We study the semi-algebraic geometry of these models, in particular their dimension, smoothness, and connectedness as well as algebraic and combinatorial properties.

Diagonal nonlinear transformations preserve structure in covariance and precision matrices

“…So distributions of this type are common test cases for non-Gaussian graph learning algorithms. They also provide a type of copula-like description of multivariate distributions: interactions (marginal and conditional independence) are specified through the covariance or the precision (or both [3]), while marginal behavior is determined with the transformation functions f i .…”