Abstract
In a model selection procedure where many models are to be compared, computational efficiency is critical. For acyclic digraph (ADG) Markov models (aka DAG models or Bayesian networks), each ADG Markov equivalence class can be represented by a unique chain graph, called an essential graph (EG). This parsimonious representation might be used to facilitate selection among ADG models. Because EGs combine features of decomposable graphs and ADGs, a scoring metric can be developed for EGs with categorical (multinomial) data. This metric may permit the characterization of local computations directly for EGs, which in turn would yield a learning procedure that does not require transformation to representative ADGs at each step for scoring purposes, nor is the scoring metric constrained by Markov equivalence.
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References
Andersson, S., Madigan, D., and Perlman, M. (1997). A characterization of Markov equivalence classes for acyclic digraphs. Annals of Statistics, 25:505–541.
Andersson, S., Madigan, D., and Perlman, M. (2001). Alternative Markov properties for chain graphs. Scandinavian Journal of Statistics, 28:33–85.
Auvray, V. and Wehenkel L. (2002). On the construction of the inclusion boundary neighborhood for Markov equivalence classes of Bayesian network structures. In Proc. of the Eighteenth Conf. on Uncertainty in Art. Int. Morgan Kaufmann.
Castelo, R. and Kočka, T. (2003). On an inclusion driven learning of Bayesian networks. Journal of Machine Learning Research, 4:527–574.
Castillo, E., Hadi, A., and Solares, C. (1997) . Learning and updating of uncertainty in Dirichlet models. Machine Learning, 26:43–63.
Chickering, D. (1996) . Learning equivalence classes of Bayesian network structures. In Proc. of the Twelfth Conf. on Uncertainty in Art. Int., pg. 150–157. Morgan Kaufmann.
Chickering, D. (2002a) . Learning equivalence classes of Bayesian-network structures. Journal of Machine Learning Research, 2:445–498.
Chickering, D. (2002b). Optimal Structure Identification with Greedy Search. Journal of Machine Learning Research, 3:507–554
Cowell, R., Dawid, A., Lauritzen, S., and Spiegelhalter, D. (1999) . Probabilistic Networks and Expert Systems. Springer-Verlag, New York.
Dawid, P. and Lauritzen, S. (1993) . Hyper-Markov laws in the statistical analysis of decomposable graphical models. Annals of Statistics, 21(3):1272–1317.
DeGroot, M. H. (1970) . Optimal Statistical Decisions. McGraw-Hill.
Frydenberg, M. (1990) . The chain graph Markov property. Scandinavian Journal of Statistics, 17:333–353.
Geiger, D. and Heckerman, D. (1998). Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Tech. Rep. MSR-TR-98–67, Oct. 1998, Microsoft Research.
Heckerman, D., Geiger, D., and Chickering, D. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20:194–243.
Kočka, T., Bouckaert, R., and Student, M. (2001). On characterizing inclusion of Bayesian networks. In Proc. of the Seventeenth Conf. on Uncertainty in Art. Int., pg. 261–268. Morgan Kaufmann.
Kočka, T. and Castelo, R. (2001) . Improved learning of Bayesian networks. In Proc. of the Seventeenth Conf. on Uncertainty in Art. Int., pg. 269–276. Morgan Kaufmann.
Lauritzen, S. (1996) . Graphical Models. Oxford University Press, Oxford.
Meek, C. (1997). Graphical models, selecting causal and statistical models. PhD Thesis, Carnegie Mellon University.
Perlman, M. (2001). Graphical model search via essential graphs. In Algebraic Methods in Statistics and Probability, V. 287, American Math. Soc, Providence, Rhode Island.
Roverato, A. and Consonni, G. (2001) . Compatible Prior Distributions for DAG models. Tech. Rep. 134, Sept. 2001, University of Pavia.
Spiegelhalter, D. and Lauritzen, S. (1990) . Sequential updating of conditional probabilities on directed graphical structures. Networks, 20:579–605.
Verma, T. and Pearl, J. (1990) . Equivalence and synthesis of causal models. In Proc. of the Sixth Conf. on Uncertainty in Art. Int., pg. 255–268. Morgan Kaufmann.
Wilks, S.S. (1962). Mathematical Statistics. Wiley, New York.
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Castelo, R., Perlman, M.D. (2004). Learning Essential Graph Markov Models from Data. In: Gámez, J.A., Moral, S., Salmerón, A. (eds) Advances in Bayesian Networks. Studies in Fuzziness and Soft Computing, vol 146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39879-0_14
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DOI: https://doi.org/10.1007/978-3-540-39879-0_14
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