Variations on undirected graphical models and their relationships

David Heckerman; Christopher Meek; Thomas Richardson

Kybernetika (2014)

  • Volume: 50, Issue: 3, page 363-377
  • ISSN: 0023-5954

Abstract

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We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case.

How to cite

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Heckerman, David, Meek, Christopher, and Richardson, Thomas. "Variations on undirected graphical models and their relationships." Kybernetika 50.3 (2014): 363-377. <http://eudml.org/doc/261918>.

@article{Heckerman2014,
abstract = {We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case.},
author = {Heckerman, David, Meek, Christopher, Richardson, Thomas},
journal = {Kybernetika},
keywords = {graphical model; undirected graph; Markov properties; Gibbs sampler; conditionally specified distributions; dependency network; graphical model; undirected graph; Markov properties; Gibbs sampler; conditionally specified distributions; dependency network},
language = {eng},
number = {3},
pages = {363-377},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Variations on undirected graphical models and their relationships},
url = {http://eudml.org/doc/261918},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Heckerman, David
AU - Meek, Christopher
AU - Richardson, Thomas
TI - Variations on undirected graphical models and their relationships
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 3
SP - 363
EP - 377
AB - We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case.
LA - eng
KW - graphical model; undirected graph; Markov properties; Gibbs sampler; conditionally specified distributions; dependency network; graphical model; undirected graph; Markov properties; Gibbs sampler; conditionally specified distributions; dependency network
UR - http://eudml.org/doc/261918
ER -

References

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  6. Heckerman, D., Chickering, D. M., Meek, C., Rounthwaite, R., Kadie, C., Dependency networks for inference, collaborative filtering, and data visualization., J. Mach. Learn. Res. 1 (2000), 49-75. Zbl1008.68132
  7. Lauritzen, S. L., Graphical Models., Clarendon Press, Oxford 1996. MR1419991
  8. Lévy, P., Chaînes doubles de Markoff et fonctions aléatoires de deux variables., C. R. Académie des Sciences, Paris 226 (1948), 53-55. Zbl0030.16601MR0023477
  9. Moussouris, J., 10.1007/BF01011714, J. Statist. Phys. 10 (1974), 11-33. MR0432132DOI10.1007/BF01011714
  10. Matúš, F., Studený, M., 10.1017/S0963548300001644, Combin. Probab. Comput. 4 (1995), 269-78. MR1356579DOI10.1017/S0963548300001644
  11. Norris, J. R., Markov Chains., Cambridge University Press, Cambridge 1997. Zbl1274.60244MR1600720
  12. Yang, E., Ravikumar, P., Allen, G. I., Liu, Z., Graphical Models via Generalized Linear Models., In: Advances in Neural Information Processing Systems 25 (2013), Cambridge. 

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