Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs

Journal of Machine Learning Research

Volumn 16, Issue , 2015, Pages 2589-2609

  He, Yangbo ^a   Jia, Jinzhu ^a   Yu, Bin ^b  

^a PEKING UNIVERSITY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Causality; Directed acyclic graphs; Markov equivalence class; Size distribution

Indexed keywords

DIRECTED GRAPHS; FUNCTIONS; GRAPH THEORY; INFORMATION DISSEMINATION; SIZE DISTRIBUTION;

AVERAGE SIZE; CAUSALITY; DIRECTED ACYCLIC GRAPH (DAG); EDGE DISTRIBUTION; GRAPH REPRESENTATION; LEARNING METHODS; MARKOV EQUIVALENCE CLASS; OBSERVATIONAL DATA;

EQUIVALENCE CLASSES;

EID: 84961666299     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. S. A. Andersson, D. Madigan, and M. D. Perlman. A characterization of Markov equivalence classes for acyclic digraphs. The Annals of Statistics, 25(2):505-541, 1997.
2. R. Castelo and M. D. Perlman. Learning essential graph Markov models from data. Studies in Fuzziness and Soft Computing, 146:255-270, 2004.
3. D. M. Chickering. Learning equivalence classes of Bayesian-network structures. The Journal of Machine Learning Research, 2:445-498, 2002.
4. M. Finegold and M. Drton. Robust graphical modeling of gene networks using classical and alternative t-distributions. The Annals of Applied Statistics, 5(2A):1057-1080, 2011.
5. N. Friedman. Inferring cellular networks using probabilistic graphical models. Science Signaling, 303(5659):799, 2004.
6. S.B. Gillispie and M.D. Perlman. The size distribution for Markov equivalence classes of acyclic digraph models. Artificial Intelligence, 141(1-2):137-155, 2002.
7. Yangbo He and Zhi Geng. Active learning of causal networks with intervention experiments and optimal designs. Journal of Machine Learning Research, 9:2523-2547, 2008.
8. Yangbo He, Jinzhu Jia, and Bin Yu. Reversible mcmc on markov equivalence classes of sparse directed acyclic graphs. The Annals of Statistics, 41(4):1742-1779, 2013a.
9. Yangbo He, Jinzhu Jia, and Bin Yu. Supplement to "reversible mcmc on markov equivalence classes of sparse directed acyclic graphs". arXiv preprint arXiv:1303.0632, 2013b.
10. D. Heckerman, C. Meek, and G. Cooper. A Bayesian approach to causal discovery. Computation, Causation, and Discovery, pages 143-67, 1999.
11. R. Jansen, H. Yu, D. Greenbaum, Y. Kluger, N.J. Krogan, S. Chung, A. Emili, M. Snyder, J.F. Greenblatt, and M. Gerstein. A Bayesian networks approach for predicting proteinprotein interactions from genomic data. Science, 302(5644):449, 2003.
12. M. H. Maathuis, M. Kalisch, and P. Bühlmann. Estimating high-dimensional intervention effects from observational data. The Annals of Statistics, 37(6A):3133-3164, 2009. ISSN 0090-5364.
13. C. Meek. Causal inference and causal explanation with background knowledge. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, pages 403-410, 1995.
14. S. Meganck, P. Leray, and B. Manderick. Learning causal bayesian networks from observations and experiments: A decision theoretic approach. In Modeling Decisions for Artificial Intelligence, pages 58-69. Springer, 2006.
15. J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge Univ Pr, 2000.
16. M.D. Perlman. Graphical model search via essential graphs. Contemporary Mathematics, 287:255-266, 2001.
17. P. Spirtes, C.N. Glymour, and R. Scheines. Causation, Prediction, and Search. The MIT Press, 2001.
18. R. E. Tarjan and M. Yannakakis. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing, 13:566, 1984.
19. T. Verma. A linear-time algorithm for finding a consistent expansion of a partially oriented graph, ". Technical report, Technical Report R-180, UCLA Cognitive Systems Laboratory, 1992.
20. T. Verma and J. Pearl. Equivalence and synthesis of causal models. In Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence, page 270. Elsevier Science Inc., 1990.