An evolutionary algorithmic approach to learning a Bayesian network from complete data

Discovering relationships between variables is crucial for interpreting data from large databases. Relationships between variables can be modeled using a Bayesian network. The challenge of learning a Bayesian network from a complete dataset grows exponentially with the number of variables in the database and the number of states in each variable. It therefore becomes important to identify promising heuristics for exploring the space of possible networks. This paper utilizes an evolutionary algorithmic approach, Particle Swarm Optimization (PSO) to perform this search. A fundamental problem with a search for a Bayesian network is that of handling cyclic networks, which are not allowed. This paper explores the PSO approach, handling cyclic networks in two different ways. Results of network extraction for the well-studied ALARM network are presented for PSO simulations where cycles are broken heuristically at each step of the optimization and where networks with cycles are allowed to exist as candidate solutions, but are assigned a poor fitness. The results of the two approaches are compared and it is found that allowing cyclic networks to exist in the particle swarm of candidate solutions can dramatically reduce the number of objective function evaluations required to converge to a target fitness value.