A New Polynomial Time Algorithm for Bayesian Network Structure Learning

2006 ◽  
pp. 501-508
Author(s):  
Sanghack Lee ◽  
Jihoon Yang ◽  
Sungyong Park
Keyword(s):  
Bayesian Network ◽  
Polynomial Time ◽  
Network Structure ◽  
Structure Learning ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Bayesian Network Structure ◽  
Bayesian Network Structure Learning

scholarly journals Parameterized Complexity Results for Exact Bayesian Network Structure Learning

2013 ◽  
Vol 46 ◽  
pp. 263-302 ◽  
Author(s):  
S. Ordyniak ◽  
S. Szeider
Keyword(s):  
Bayesian Network ◽  
Polynomial Time ◽  
Network Structure ◽  
Structure Learning ◽  
Training Data ◽  
Worst Case ◽  
Super Structure ◽  
Bounded Treewidth ◽  
Bayesian Network Structure ◽  
Bayesian Network Structure Learning

Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure. The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-based Bayesian network structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian network structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth, and in linear time if in addition the super-structure has bounded maximum degree. Furthermore, we show that if the directed super-structure is acyclic, then exact Bayesian network structure learning can be carried out in quadratic time. We complement these positive results with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Similarly, exact Bayesian network structure learning remains NP-hard for "almost acyclic" directed super-structures. Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).

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