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Języki publikacji
Abstrakty
We show that if a strictly positive joint probability distribution for a set of binary variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is show to hold also for multivariate nondegenerate normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probabilisty distributions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
231--239
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Computer Science Department, Technion, Haifa, 32000 Israel
autor
- Computer Science Department, Technion, Haifa, 32000 Israel
autor
- Microsoft Research, Redmond, WA, 98052, U.S.A.
Bibliografia
- [1] C. Chow and C. Liu, Approximating discrete probability distributions with dependence trees, IEEE Trans. Inform. Theory 14 (1968), pp. 462-467.
- [2] A. P. Dawid, Conditional independence in statistical theory (with discussion), J. Roy. Statist. Soc. Ser. B 41 (1979), pp. 1-31.
- [3] D. Geiger and J. Pearl, Logical and algorithmic properties of conditional independence and graphical models, Ann. Statist 21 (1993), pp. 2001-2021.
- [4] C. Glymour and G. Cooper, Computation, Causation, Discovery, AAAI press/The MIT press, Menlo Park 1999.
- [5] S. Lauritzen, Lectures on Contingency Tables, 3rd edition, Aalborg University, 1989.
- [6] S. Lauritzen and D. Spiegelhalter, Local computations .with probabilities on graphical structures and their application to expert systems (with discussion), J. Roy. Statist. Soc. Ser. B 50 (1988), pp. 157-224.
- [7] F. Matúš, On equivalence of Markov properties ouer undirected graphs, J. Appl. Probab. 29 (1992), pp. 745-749.
- [8] C. Meek, Graphical Models: Selecting Causal and Statistical Models, Ph. D. Thesis, Carnegie Mellon University, 1997.
- [9] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, California, 1988.
- [10] J. Pearl and A. Paz, Graphoids: a graph based logic for reasoning about relevancy relations, in: Advances in Artificial Intelligence. II, B. Boulay, D. Hogg and L. Steel (Eds.), North-Holland, Amsterdam 1985, pp. 357-363. See also Pearl (1988), p. 139.
- [11] R. Settimi and J. Smith, Geometry, moments and bayesian networks with hidden variables in: Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, Morgan Kaufmann, San Francisco 1999, pp. 293-298.
- [12] W. Spohn, Stochastic independence, causal independence, and shieldability, J. Philos. Logic 9 (1980), pp. 73-99.
- [13] M. Studeny, Conditional independences have no finite complete characterization, in: Transactions of the 11 th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Academia, Prague 1992, pp. 3-16.
- [14] J. Whittaker, Graphical Models in Applied Multivariate Statistics, Wiley, Chichester 1990.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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