A Birth and Death Process for Bayesian Network Structure Inference

TL;DR

This paper introduces a birth and death process model for Bayesian network structure inference, offering an alternative to traditional search methods with improved mixing properties.

Contribution

It proposes a novel birth and death process approach for BN structure learning, demonstrating its advantages over Metropolis-Hastings.

Findings

Birth and death process shows superior mixing properties.

Empirical evidence favors the new approach over traditional methods.

Improved efficiency in exploring BN structures.

Abstract

Bayesian networks (BNs) are graphical models that are useful for representing high-dimensional probability distributions. There has been a great deal of interest in recent years in the NP-hard problem of learning the structure of a BN from observed data. Typically, one assigns a score to various structures and the search becomes an optimization problem that can be approached with either deterministic or stochastic methods. In this paper, we walk through the space of graphs by modeling the appearance and disappearance of edges as a birth and death process and compare our novel approach to the popular Metropolis-Hastings search strategy. We give empirical evidence that the birth and death process has superior mixing properties.