A Transformational Characterization of Equivalent Bayesian Network Structures

TL;DR

This paper introduces a simple local transformation-based characterization of equivalent Bayesian network structures, enabling efficient identification of compelled edges crucial for causal inference and structure learning.

Contribution

It provides a new, straightforward characterization of Bayesian network equivalence and an algorithm to identify compelled edges, advancing structure learning methods.

Findings

New invariant properties of equivalent structures

Efficient algorithm for compelled edge identification

Enhanced understanding of causal relationships in Bayesian networks

Abstract

We present a simple characterization of equivalent Bayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily prove several new invariant properties of theoretical interest for equivalent structures. Second, we use the characterization to derive an efficient algorithm that identifies all of the compelled edges in a structure. Compelled edge identification is of particular importance for learning Bayesian network structures from data because these edges indicate causal relationships when certain assumptions hold.