On factorization of probability distributions over directed graphs

František Matúš; Bernhard Strohmeier

Kybernetika (1998)

  • Volume: 34, Issue: 1, page [57]-68
  • ISSN: 0023-5954

Abstract

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Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple, strict edge-subgraphs. This gives sometimes the possibility to break circuits and get back to the acyclic, well-understood case.

How to cite

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Matúš, František, and Strohmeier, Bernhard. "On factorization of probability distributions over directed graphs." Kybernetika 34.1 (1998): [57]-68. <http://eudml.org/doc/33334>.

@article{Matúš1998,
abstract = {Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple, strict edge-subgraphs. This gives sometimes the possibility to break circuits and get back to the acyclic, well-understood case.},
author = {Matúš, František, Strohmeier, Bernhard},
journal = {Kybernetika},
keywords = {factorizability; directed graph; factorizability; directed graph},
language = {eng},
number = {1},
pages = {[57]-68},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On factorization of probability distributions over directed graphs},
url = {http://eudml.org/doc/33334},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Matúš, František
AU - Strohmeier, Bernhard
TI - On factorization of probability distributions over directed graphs
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 1
SP - [57]
EP - 68
AB - Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple, strict edge-subgraphs. This gives sometimes the possibility to break circuits and get back to the acyclic, well-understood case.
LA - eng
KW - factorizability; directed graph; factorizability; directed graph
UR - http://eudml.org/doc/33334
ER -

References

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  6. Koster J. T. A., 10.1214/aos/1069362315, Ann. Statist. 24 (1996), 2148–2177 (1996) MR1421166DOI10.1214/aos/1069362315
  7. Spirtes P., Directed cyclic graphical representation of feedback models, In: Proceedings of the Eleventh Conference on Uncertainty and Artificial Inteligence (P. Besnard and S. Hanks, eds.), Morgan Kaufman Publ. Inc., San Mateo 1995 
  8. Strohmeier B., Cyclical Causal Networks and Knowledge Integration, Ph.D. Dissertation. Fakultät für Wirtschaftswissenschaften, Universität Bielefeld 1996 
  9. Vajda I., Theory of Statistical Inference and Information, Kluwer Academic Publishers, Dordrecht – Boston – London 1989 Zbl0711.62002
  10. Whittaker J., Graphical Models in Applied Multivariate Statistics, J. Wiley, New York 1990 Zbl1151.62053MR1112133

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