Normal binary graph models

TL;DR

This paper characterizes when the marginal semigroup of a binary graph model is normal, linking it to the absence of K_4 minors in the graph, and explores implications for algebraic statistics.

Contribution

It provides a complete characterization of normality for binary graph models based on graph minors, connecting algebraic and geometric properties.

Findings

Normality of the marginal semigroup is equivalent to the graph being K_4 minor-free.

The approach uses the interplay between normality and the geometry of the marginal cone.

Potential applications to other normality questions in algebraic statistics.

Abstract

We show that the marginal semigroup of a binary graph model is normal if and only if the graph is free of K_4 minors. The technique, based on the interplay of normality and the geometry of the marginal cone, has potential applications to other normality questions in algebraic statistics.