Learning non probabilistic belief networks
Probability intervals constitute an interesting formalism for representing uncertainty. In order to use them together with belief networks, we study basic concepts as marginalization, conditioning and independence for probability intervals. Then we develop some algorithms for learning simple belief networks (trees and polytrees), based on this kind of non purely probabilistic information.
Unable to display preview. Download preview PDF.
- 1.S. Acid, L.M. de Campos, A. González, R. Molina, N. Pérez de la Blanca: Learning with CASTLE, in Symbolic and Quantitative Approaches to Uncertainty, Lecture Notes in Computer Science 548, R. Kruse, P. Siegel (Eds.), Springer Verlag (1991) 99–106Google Scholar
- 2.L.M. de Campos, M.T. Lamata, S. Moral: Logical connectives for combining fuzzy measures, in Methodologies for Intelligent Systems 3, Z.W. Ras, L. Saitta (Eds.), North-Holland, New York (1988) 11–18Google Scholar
- 3.L.M. de Campos, M.T. Lamata, S. Moral: The concept of conditional fuzzy measure, International Journal of Intelligent Systems 5 (1990) 237–246Google Scholar
- 4.J.E. Cano, S. Moral, J.F. Verdegay: Propagation of convex sets of probabilities in directed acyclic networks, Proceedings of the Fourth IPMU Conference (1992) 289–292Google Scholar
- 5.C.K. Chow, C.N. Liu: Approximating discrete probability distribution with dependence trees, IEEE Transactions on Information Theory 14 (1968) 462–467Google Scholar
- 6.G.F. Cooper, E. Herskovits: A Bayesian Method for the Induction of Probabilistic Networks from Data, Machine Learning 9 (1992) 309–347Google Scholar
- 7.H.E. Kyburg: Bayesian and non-bayesian evidential updating, Artificial Intelligence 31 (1987) 271–293Google Scholar
- 8.S.L. Lauritzen, D.J. Spiegelhalter: Local Computations with probabilities on graphical structures and their applications to expert systems, Journal of the Royal Statistical Society B-50 (1988) 157–224Google Scholar
- 9.J. Pearl: Probabilistic reasoning in intelligent systems: networks of plausible inference, Morgan and Kaufmann, San Mateo (1988)Google Scholar
- 10.G. Rebane, J. Pearl: The recovery of causal poly-trees from statistical data, in Uncertainty in Artificial Intelligence 3, L.N. Kanal, T.S. Levitt and J.F. Lemmer (Eds.), North-Holland (1989) 175–182Google Scholar
- 11.G. Shafer, P.P. Shenoy: Axioms for probability and belief function propagation, in Uncertainty in Artificial Intelligence 4, R.D. Shachter, T.S. Levitt, L.N. Kanal, J.F. Lemmer (Eds.), North-Holland, Amsterdam (1990) 169–198Google Scholar
- 12.P. Spirtes: Detecting causal relations in the presence of unmeasured variables, Uncertainty in Artificial Intelligence, Proc. of the Seventh Conference (1991) 392–397Google Scholar
- 13.B. Tessem: Interval representation on uncertainty in Artificial Intelligence, Ph. D. Thesis, Department of Informatics, University of Bergen, Norway (1989)Google Scholar