Bayesian Networks from the Point of View of Chain Graphs

TL;DR

This paper advocates using chain graphs to represent probabilistic independence, showing their equivalence to Bayesian networks and proposing a unified, memory-efficient factorization method based on the largest chain graph.

Contribution

It introduces a graphical characterization of chain graphs, defines the largest chain graph for equivalence classes, and proposes a new factorization approach for discrete distributions.

Findings

Chain graphs can effectively represent Bayesian network structures.

The largest chain graph provides a unified factorization basis.

A simplified separation criterion for chain graphs is developed.

Abstract

AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with respect to a chain graph which is Markov equivalent to the Bayesian network. A graphical characterization of such graphs is given. The class of equivalent graphs can be represented by a distinguished graph which is called the largest chain graph. The factorization formula with respect to the largest chain graph is a basis of a proposal of how to represent the corresponding (discrete) probability distribution in a computer (i.e. parametrize it). This way does not depend on the choice of a particular Bayesian network from the class of equivalent networks and seems to be the most efficient way from the point of view of memory demands. A separation criterion for reading independency statements from a chain graph is formulated in a simpler way. It resembles the well-known d-separation criterion for Bayesian networks and can be implemented locally.