Optimal search on clustered structural constraint for learning bayesian network structure

Kaname Kojima, Eric Perrier, Seiya Imoto, Satoru Miyano, David Maxwell Chickering

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


We study the problem of learning an optimal Bayesian network in a constrained search space; skeletons are compelled to be subgraphs of a given undirected graph called the super-structure. The previously derived constrained optimal search (COS) remains limited even for sparse superstructures. To extend its feasibility, we propose to divide the super-structure into several clusters and perform an optimal search on each of them. Further, to ensure acyclicity, we introduce the concept of ancestral constraints (ACs) and derive an optimal algorithm satisfying a given set of ACs. Finally, we theoretically derive the necessary and sufficient sets of ACs to be considered for finding an optimal constrained graph. Empirical evaluations demonstrate that our algorithm can learn optimal Bayesian networks for some graphs containing several hundreds of vertices, and even for super-structures having a high average degree (up to four), which is a drastic improvement in feasibility over the previous optimal algorithm. Learnt networks are shown to largely outperform state-of-the-art heuristic algorithms both in terms of score and structural hamming distance.

Original languageEnglish
Pages (from-to)285-310
Number of pages26
JournalJournal of Machine Learning Research
Publication statusPublished - 2010 Feb 22
Externally publishedYes


  • Bayesian networks
  • Constrained optimal search
  • Structure learning

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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