Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Algorithm 515: Generation of a Vector from the Lexicographical Index [G6]
ACM Transactions on Mathematical Software (TOMS)
Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
Exact structure discovery in Bayesian networks with less space
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Parallel globally optimal structure learning of Bayesian networks
Journal of Parallel and Distributed Computing
Finding optimal Bayesian networks using precedence constraints
The Journal of Machine Learning Research
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We present a parallel algorithm for the score-based optimal structure search of Bayesian networks. This algorithm is based on a dynamic programming (DP) algorithm having O(n ⋅ 2n) time and space complexity, which is known to be the fastest algorithm for the optimal structure search of networks with n nodes. The bottleneck of the problem is the memory requirement, and therefore, the algorithm is currently applicable for up to a few tens of nodes. While the recently proposed algorithm overcomes this limitation by a space-time trade-off, our proposed algorithm realizes direct parallelization of the original DP algorithm with O(nσ) time and space overhead calculations, where σ0 controls the communication-space trade-off. The overall time and space complexity is O(nσ+1 2n). This algorithm splits the search space so that the required communication between independent calculations is minimal. Because of this advantage, our algorithm can run on distributed memory supercomputers. Through computational experiments, we confirmed that our algorithm can run in parallel using up to 256 processors with a parallelization efficiency of 0.74, compared to the original DP algorithm with a single processor. We also demonstrate optimal structure search for a 32-node network without any constraints, which is the largest network search presented in literature.