The geometry of Gaussian double Markovian distributions

TL;DR

This paper explores the geometric and algebraic properties of Gaussian double Markovian models, which impose zero constraints on both covariance matrices and their inverses based on graph structures.

Contribution

It provides a detailed analysis of the semi-algebraic geometry, including dimension, smoothness, and connectedness, of these models, highlighting their algebraic and combinatorial characteristics.

Findings

Characterization of the dimension of Gaussian double Markovian models

Analysis of smoothness and connectedness properties

Identification of algebraic and combinatorial features

Abstract

Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance 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.