A Graph-Based Inference Method for Conditional Independence

TL;DR

This paper introduces a graphical inference method for conditional independence, using multiple undirected graphs and transformations, providing a purely graphical proof technique aligned with graphoid axioms.

Contribution

It presents a novel graphical representation and transformation system for deriving conditional independence statements, avoiding numerical calculations.

Findings

Graphical system equivalent to graphoid axioms

Purely graphical proof technique for conditional independence

Representation using multiple undirected graphs

Abstract

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.