Joe Johnson: Equivalence of Graphical Models through Toric Geometry

Abstract

In the study of (possibly cyclic) directed graphical models, one aims to understand how the structure of a directed graph relates to the structure of an associated model. Many graphs yield the same model — a feature called distribution equivalence. In the acyclic case, equivalent graphs are related via a sequence of covered edge flips. We translate these edge flips into generators of a binomial ideal and apply the theory of binomial and toric ideals to study distribution equivalence of cyclic graphical models.