Reading Dependencies from Polytree-Like Bayesian Networks

TL;DR

This paper introduces a graphical criterion for identifying dependencies in polytree-like Bayesian networks, proving its soundness and completeness under certain assumptions, which broadens understanding of dependency structures.

Contribution

It provides a new, proven graphical criterion for reading dependencies from minimal directed independence maps in polytree Bayesian networks under specific conditions.

Findings

The criterion is sound and complete.

Assumptions of composition and weak transitivity are justified.

Applicable to polytree structures in Bayesian networks.

Abstract

We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p when G is a polytree and p satisfies composition and weak transitivity. We prove that the criterion is sound and complete. We argue that assuming composition and weak transitivity is not too restrictive.