A Birth and Death Process for Bayesian Network Structure Inference

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.