A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks
This work is incremental, extending prior research to provide a tool for empirically studying heuristic algorithms and the adequacy of the MDL principle in learning Bayesian networks.
The paper tackles the problem of learning Bayesian network structures by presenting a depth-first branch-and-bound algorithm based on the minimum description length (MDL) principle, which guarantees to find the optimal network for a given variable ordering, with preliminary experiments showing efficient performance and slow time complexity growth with sample size.
This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent) variable ordering. The algorithm exhaustively searches through all network structures and guarantees to find the network with the best MDL score. Preliminary experiments show that the algorithm is efficient, and that the time complexity grows slowly with the sample size. The algorithm is useful for empirically studying both the performance of suboptimal heuristic search algorithms and the adequacy of the MDL principle in learning Bayesian networks.