A geometric view on learning Bayesian network structures

International Journal of Approximate Reasoning

Volumn 51, Issue 5, 2010, Pages 573-586

  Studený, Milan ^a   Vomlel, Jiří ^a   Hemmecke, Raymond ^b  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Geometric neighborhood; GES algorithm; Inclusion neighborhood; Learning Bayesian networks; Standard imset

Indexed keywords

BARIUM COMPOUNDS; GEOMETRY;

AFFINE FUNCTION; ALGEBRAIC APPROACHES; EXTREME POINTS; GEOMETRIC NEIGHBORHOOD; LEARNING BAYESIAN NETWORKS; MARKOVIAN DISTRIBUTION; SEARCH TECHNIQUE; STANDARD IMSET;

BAYESIAN NETWORKS;

EID: 77955230142     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2010.01.014     Document Type: Conference Paper

References (22)

1. 4ti2 team, 4ti2, a software package for algebraic, geometric and combinatorial problems on linear spaces. Available at < http://www.4ti2.de.
2. S.A. Andersson, D. Madigan, and M.D. Perlman A characterization of Markov equivalence classes for acyclic digraphs The Annals of Statistics 25 1997 505 541
3. R.R. Bouckaert, Bayesian belief networks: from construction to evidence, Ph.D. Thesis, University of Utrecht, 1995.
4. A. Brøndsted An Introduction to Convex Polytopes 1983 Springer-Verlag
5. D.M. Chickering Optimal structure identification with greedy search Journal of Machine Learning Research 3 2002 507 554
6. M. Franz, Convex, a Maple package for convex geometry. Available at < http://www.math.uwo.ca/~mfranz/convex.
7. K. Fukuda, cdd and cdd+, an implementation of the double description method. Available at < http://www.ifor.math.ethz.ch/~fukuda/cdd-home/cdd. html.
8. M. Frydenberg The chain graph Markov property Scandinavian Journal of Statistics 17 1990 333 353
9. D. Geiger, and J. Pearl On the logic of causal models Proceedings of the 4th Conference on Uncertainty in Artificial Intelligence 1990 North-Holland 3 14
10. Ilog team, Cplex, mathematical programming optimizer, version 10.1. Available at < www.ilog.com/products/cplex.
11. S.L. Lauritzen Graphical Models 1996 Clarendon Press
12. C. Meek, Graphical models, selecting causal and statistical models, Ph.D. Thesis, Carnegie Melon University, 1997.
13. R.E. Neapolitan Learning Bayesian Networks 2004 Pearson Prentice Hall
14. J. Pearl Probabilistic Reasoning in Intelligent Systems 1988 Morgan Kaufmann
15. A. Schrijver Theory of Linear and Integer Programming 1986 John Wiley
16. G. Schwarz Estimation the dimension of a model The Annals of Statistics 6 1978 461 464
17. T. Silander, and P. Myllymäki A simple approach for finding the globally optimal Bayesian network structure Proceedings of the 22th Conference on Uncertainty in Artificial Intelligence 2006 AUAI Press 445 452
18. M. Studený Probabilistic Conditional Independence Structures 2005 Springer-Verlag
19. M. Studený, and J. Vomlel A reconstruction algorithm for the essential graph International Journal of Approximate Reasoning 50 2009 385 413
20. T. Verma, and J. Pearl Equivalence and synthesis of causal models Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence 1991 Elsevier 220 227
21. J. Vomlel, M. Studený, Geometric neighborhood for Bayesian network structures over three and four variables, 2008. Web page, see < http://www.utia.cas.cz/vomlel/imset/polytopes-3v-and-4v.html.
22. G.M. Ziegler Lectures on Polytopes 1995 Springer-Verlag