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Tractable Bayesian Network Structure Learning with Bounded Vertex Cover Number
lib:f0c068492ca40d11 (v1.0.0)
Authors: Janne H. Korhonen,Pekka Parviainen
Where published: NeurIPS 2015 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/6003-tractable-bayesian-network-structure-learning-with-bounded-vertex-cover-number
Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width~2. In this paper, we propose bounded vertex cover number Bayesian networks as an alternative to bounded tree-width networks. In particular, we show that both inference and learning can be done in polynomial time for any fixed vertex cover number bound $k$, in contrast to the general and bounded tree-width cases; on the other hand, we also show that learning problem is W[1]-hard in parameter $k$. Furthermore, we give an alternative way to learn bounded vertex cover number Bayesian networks using integer linear programming (ILP), and show this is feasible in practice.
Where published: NeurIPS 2015 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/6003-tractable-bayesian-network-structure-learning-with-bounded-vertex-cover-number
Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width~2. In this paper, we propose bounded vertex cover number Bayesian networks as an alternative to bounded tree-width networks. In particular, we show that both inference and learning can be done in polynomial time for any fixed vertex cover number bound $k$, in contrast to the general and bounded tree-width cases; on the other hand, we also show that learning problem is W[1]-hard in parameter $k$. Furthermore, we give an alternative way to learn bounded vertex cover number Bayesian networks using integer linear programming (ILP), and show this is feasible in practice.
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