Abstract
Main problems connected with application of probabilistic methods in AI are those arising from high computational complexity of algorithms. Problems of practical importance are of high dimensionality (hundreds or even thousands of variables) which brings necessity to cope with a question how to handle such multidimensional probability distributions. The answer lies in utilizing special classes of distributions (log-linear, graphical, decomposable or some others) which makes possible to recontruct the distributions from a reasonable number of parameters. The present text makes an introduction to some of these techniques.
Preview
Unable to display preview. Download preview PDF.
References
C. Berge: Graphs and hypergraphs. North-Holland, Amsterdam, 1973
P. Cheeseman: A method of computing generalized Bayesian probability values for expert systems. In: Proc. 6th Int. Conf. on AI (IJCAI 83), Karlsruhe, FRG, 1983, pp 198–202
P. Cheeseman: In defense of probability. In: Proc. 8th Int. Conf. on AI (IJCAI 85), Los Angeles, CA, 1985, pp 1002–1007
I. Csiszár: I-divergence geometry of probability distributions and minimization problems. Ann. Probab., 3, pp 146–158 (1975)
W.E. Deming, F.F. Stephan: On a least square adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Stat., 11, pp 427–444 (1940)
D. Geiger, J. Pearl: On the logic of influence diagrams. In: Proc. 4th Workshop on Uncertainty in AI, Minneapolis, MN, 1988
P. Hájek, T. Havránek, R. Jiroušek: Uncertain Information Processing in Expert Systems. CRC Press, Inc., 1992
R. Jiroušek: A survey of methods used in probabilistic expert systems for knowledge integration. Knowledge-Based Systems, 3, pp 7–12 (1990)
R. Jiroušek: Computational aspects of knowledge integration process in probabilistic expert systems. Comput. Stat. Quarterly, 4, pp 299–306 (1990)
R. Jiroušek: Reasoning and derivation of knowledge in probabilistic expert systems. To appear in: Trans of the 11th Prague Conference on Inf. Theory, etc., Prague, CSFR
R. Jiroušek: Decision trees and their power to represent probability distributions. In: Proceedings of the 2nd Workshop on Uncertainty Processing in Expert Systems, Alšovice, CSFR, 1991
R. Jiroušek: Solution of the marginal problem and decomposable distributions. Kybernetika, 27, pp 403–412 (1991)
J.H. Kim, J. Pearl: A computational model for combined causal and diagnostic reasoning in inference systems. In: Proc. 8th Int. Conf. on AI (IJCAI 85), Los Angeles, CA, 1985, pp 190–195
S.L. Lauritzen, D. Spiegelhalter: Local computations with probabilities on graphical structures and their applications to expert systems. J. Roy. Stat. Soc. Ser. B., 50, pp 157–189 (1988)
F. M. Malvestuto: Computing the maximum-entropy extension of given discrete probability distributions. Comput. Statist. Data Anal. 8, pp 299–311 (1989)
J. Pearl: Probabilistic Reasoning in Intelligence Systems: Networks of Plausible Inference. Morgan-Kaufmann, San Mateo, CA 1988
J. Pearl, A. Paz: GRAPHOIDS: A Graph-Based Logic for Reasoning about Relevance Relations. TR850038 (R-53) UCLA Computer Science Dept. (1988)
J. Pearl, M. Tarsi: Structuring causal trees. J. Complexity, 2, pp 60–69 (1986)
A. Perez: ε-admissible simplification of the dependence structure of a set of random variables. Kybernetika, 13, pp 439–450 (1977)
A. Perez: A probabilistic approach to the integration of partial knowledge for medical decision-making, (in Czech) In: Proc. 1st Czechoslovak Congress of Biomed. Eng. (BMI 83), Mariánské Lázně, CSFR, 1983, pp 221–226
D.J. Rose, R.E. Tarjan, G.S. Luoker: Algorithmic approach at vertex elimination on graphs. SIAM J. Comput., 5, pp 266–193 (1976)
R. D. Shachter: Evaluating influence diagrams. Operations Res., 34, pp 871–882 (1986)
R. D. Shachter: Intelligent probabilistic inference. In: L.N. Kanal, J.F. Lemmer (eds.): Uncertainty in Artificial Intelligence. North-Holland, Amsterdam, 1986
R. D. Shachter: Probabilistic inference and influence diagrams. Operations Res., 36, pp 589–604 (1988)
R.E. Tarjan, M. Yannakakis: Simple linear-time algorithms to test chordality of graphs, test acyclidity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput, 13, pp 566–591 (1984)
S. Ur, A. Paz: The representation power of probabilistic knowledge by undirected graphs and directed acyclic graphs. A comparison, In: Proceedings of the 2nd Workshop on Uncertainty Processing in Expert Systems, Alšovice, CSFR, 1991
J. Whittaker: Graphical Models in Applied Multivariate Statistics. J. Wiley, New York 1990
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiroušek, R. (1992). Introduction to probabilistic methods of knowledge representation and processing. In: Mřrík, V., Štěpánková, O., Trappl, R. (eds) Advanced Topics in Artificial Intelligence. Lecture Notes in Computer Science, vol 617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55681-8_40
Download citation
DOI: https://doi.org/10.1007/3-540-55681-8_40
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55681-7
Online ISBN: 978-3-540-47271-1
eBook Packages: Springer Book Archive