Large-sample learning of Bayesian networks is NP-hard

Journal of Machine Learning Research

Volumn 5, Issue , 2004, Pages 1287-1330

  Chickering, David Maxwell ^a   Heckerman, David ^a   Meek, Christopher ^a  

^a MICROSOFT RESEARCH   (United States)

Author keywords

Large sample data; Learning bayesian networks; NP hard; Search complexity

Indexed keywords

ALGORITHMS; COMPLEX NETWORKS; COMPUTATIONAL COMPLEXITY; LEARNING ALGORITHMS;

COMPLEXITY RESULTS; DISCRETE VARIABLES; JOINT DISTRIBUTIONS; LEARNING BAYESIAN NETWORKS; LOCAL DISTRIBUTIONS; NP-HARD; SAMPLE DATA; SEARCH COMPLEXITY;

BAYESIAN NETWORKS;

EID: 33646107783     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Bouckaert, R. R. (1995). Bayesian Belief Networks: From Construction to Inference. PhD thesis, Utrecht University, The Netherlands.
2. Chickering, D. M. (1995). A transformational characterization of Bayesian network structures. In Hanks, S. and Besnard, P., editors, Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, Montreal, QU, pages 87-98. Morgan Kaufmann.
3. Chickering, D. M. (1996). Learning Bayesian networks is NP-Complete. In Fisher, D. and Lenz, H., editors, Learning from Data: Artificial Intelligence and Statistics V, pages 121-130. Springer-Verlag.
4. Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of Machine Learning Research, 3:507-554.
5. Dasgupta, S. (1999). Learning polytrees. In Laskey, K. and Prade, H., editors, Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, Stockholm, Sweden, pages 131-141. Morgan Kaufmann.
6. Druzdzel, M. J. and Henrion, M. (1993). Efficient reasoning in qualitative probabilistic networks. In Proceedings of the Eleventh Annual Conference on Artificial Intelligence (AAAI-93), Washington, D. C., pages 548-553.
7. Garey, M. and Johnson, D. (1979). Computers and intractability: A guide to the theory of NP-completeness. W. H. Freeman.
8. Gavril, F. (1977). Some NP-complete problems on graphs. In Proc. 11th Conf. on Information Sciences and Systems, Johns Hopkins University, pages 91-95. Baltimore, MD.
9. Howard, R. and Matheson, J. (1981). Influence diagrams. In Readings on the Principles and Applications of Decision Analysis, volume II, pages 721-762. Strategic Decisions Group, Menlo Park, CA.
10. Karlin, S. and Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities. i. multivariate totally positive distributions. Journal of Multivariate Analysis, 10:467-498.
11. Meek, C. (1997). Graphical Models: Selecting causal and statistical models. PhD thesis, Carnegie Mellon University.
12. Meek, C. (2001). Finding a path is harder than finding a tree. Journal of Artificial Intelligence Research, 15:383-389.
13. Nielsen, J. D., Kočka, T., and Peña, J. M. (2003). On local optima in learning Bayesian networks. In Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence, Acapulco, Mexico, pages 435-442. Morgan Kaufmann.
14. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA.
15. Spirtes, P., Glymour, C., and Scheines, R. (2000). Causation, Prediction, and Search (second edition). The MIT Press, Cambridge, Massachussets.
16. Srebro, N. (2001). Maximum likelihood bounded tree-width Markov networks. In Breese, J. and Koller, D., editors, Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, Seattle, WA, pages 504-511. Morgan Kaufmann.
17. Wellman, M. P. (1990). Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence, 44:257-303.