Selfadhesivity in Gaussian conditional independence structures

TL;DR

This paper explores the property of selfadhesivity in Gaussian conditional independence structures, showing its relation to entropic polymatroids and positive definite matrices, and deriving new axioms for Gaussian CI.

Contribution

It introduces the concept of selfadhesivity in Gaussian CI, linking it to entropic polymatroids and positive definite matrices, and develops new axioms for Gaussian CI structures.

Findings

Positive definite matrices satisfy selfadhesivity.

Selfadhesivity leads to new axioms of Gaussian CI.

Connections between entropic polymatroids and Gaussian structures.

Abstract

Selfadhesivity is a property of entropic polymatroids which guarantees that the polymatroid can be glued to an identical copy of itself along arbitrary restrictions such that the two pieces are independent given the common restriction. We show that positive definite matrices satisfy this condition as well and examine consequences for Gaussian conditional independence structures. New axioms of Gaussian CI are obtained by applying selfadhesivity to the previously known axioms of structural semigraphoids and orientable gaussoids.