Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact Algorithms for Exact Satisfiability and Number of Perfect Matchings
Algorithmica - Parameterized and Exact Algorithms
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Efficient Structure Learning of Bayesian Networks using Constraints
The Journal of Machine Learning Research
Parallel Algorithm for Learning Optimal Bayesian Network Structure
The Journal of Machine Learning Research
Searching optimal bayesian network structure on constraint search space: super-structure approach
JSAI-isAI'10 Proceedings of the 2010 international conference on New Frontiers in Artificial Intelligence
Learning bayesian networks from Markov random fields: An efficient algorithm for linear models
ACM Transactions on Knowledge Discovery from Data (TKDD)
International Journal of Approximate Reasoning
Finding optimal Bayesian networks using precedence constraints
The Journal of Machine Learning Research
Learning optimal bayesian networks: a shortest path perspective
Journal of Artificial Intelligence Research
| Hi-index | 0.00 |
The fastest known exact algorithms for score-based structure discovery in Bayesian networks on n nodes run in time and space 2nnO(1). The usage of these algorithms is limited to networks on at most around 25 nodes mainly due to the space requirement. Here, we study space--time tradeoffs for finding an optimal network structure. When little space is available, we apply the Gurevich--Shelah recurrence---originally proposed for the Hamiltonian path problem---and obtain time 22n-snO(1) in space 2snO(1) for any s = n/2, n/4, n/8, ...; we assume the indegree of each node is bounded by a constant. For the more practical setting with moderate amounts of space, we present a novel scheme. It yields running time 2n(3/2)pnO(1) in space 2n(3/4)pnO(1) for any p = 0, 1, ..., n/2; these bounds hold as long as the indegrees are at most 0.238n. Furthermore, the latter scheme allows easy and efficient parallelization beyond previous algorithms. We also explore empirically the potential of the presented techniques.