Local and Global Algorithms for Learning Dynamic Bayesian Networks

Learning optimal Bayesian networks (BN) from data is NP-hard in general. Nevertheless, certain BN classes with additional topological constraints, such as the dynamic BN (DBN) models, widely applied in specific fields such as systems biology, can be efficiently learned in polynomial time. Such algorithms have been developed for the Bayesian-Dirichlet (BD), Minimum Description Length (MDL), and Mutual Information Test (MIT) scoring metrics. The BD-based algorithm admits a large polynomial bound, hence it is impractical for even modestly sized networks. The MDL-and MIT-based algorithms admit much smaller bounds, but require a very restrictive assumption that all variables have the same cardinality, thus significantly limiting their applicability. In this paper, we first propose an improvement to the MDL-and MIT-based algorithms, dropping the equicardinality constraint, thus significantly enhancing their generality. We also explore local Markov blanket based algorithms for constructing BN in the context of DBN, and show an interesting result: under the faithfulness assumption, the mutual information test based local Markov blanket algorithms yield the same network as learned by the global optimization MIT-based algorithm. Experimental validation on small and large scale genetic networks demonstrates the effectiveness of our proposed approaches.