A Transformational Characterization of Equivalent Bayesian Network Structures
This work addresses a theoretical bottleneck in Bayesian network learning, enabling more efficient causal analysis, though it is incremental in nature.
The paper tackles the problem of characterizing equivalent Bayesian network structures using local transformations, resulting in new invariant properties and an efficient algorithm for identifying compelled edges, which are crucial for causal inference in structure learning.
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.