On the use of local search heuristics to improve GES-based Bayesian network learning

Bayesian networks learning is computationally expensive even in the case of sacrificing the optimality of the result. Many methods aim at obtaining quality solutions in affordable times. Most of them are based on local search algorithms, as they allow evaluating candidate networks in a very efficient way, and can be further improved by us ing local search-based metaheuristics to avoid getting stuck in local optima. This approach has been successfully applied in searching for network structures in the space of directed acyclic graphs. Other algorithms search for the networks in the space of equiva lence classes. The most important of these is GES (Greedy Equiv alence Search). It guarantees obtaining the optimal network under certain conditions. However, it can also get stuck in local optima when learning from datasets with limited size. This article proposes the use of local search-based metaheuristics as a way to improve the behaviour of GES in such circumstances. These methods also guar antee asymptotical optimality, and the experiments show that they improve upon the score of the networks obtained with GES

Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data

We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form parameter estimates, and eliminates the need for inference in a Bayesian network. Our approach provides consistent parameter estimates for missing data problems that are MCAR, MAR, and in some cases, MNAR. Empirically, our approach is orders of magnitude faster than EM (as our approach requires no inference). Given sufficient data, we learn parameters that can be orders of magnitude more accurate