×

zbMATH — the first resource for mathematics

Possibilistic conditional independence: A similarity-based measure and its application to causal network learning. (English) Zbl 0941.68120
Summary: A definition for similarity between possibility distributions is introduced and discussed as a basis for detecting dependence between variables by measuring the similarity degree of their respective distributions. This definition is used to detect conditional independence relations in possibility distributions derived from data. This is the basis for a new hybrid algorithm for recovering possibilistic causal networks. The algorithm POSSCAUSE is presented and its applications discussed and compared with analogous developments in possibilistic and probabilistic causal networks learning.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
Software:
UCI-ml
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Beinlich, I.A.; Suermondt, H.J.; Chavez, R.M.; Cooper, G.F., The ALARM monitoring system: A case study with two probabilistic inference techniques, (), 247-256
[2] Bouckaert, R.R., Bayesian belief networks: from construction to inference, ()
[3] Cano, J.E.; Delgado, M.; Moral, S., An axiomatic framework for the propagation of uncertainty in directed acyclic graphs, International journal of approximate reasoning, 8, 253-280, (1993) · Zbl 0777.68071
[4] Chow, C.K.; Liu, C.N., Approximating discrete probability distributions with dependence trees, IEEE transactions on information theory, 14, 462-467, (1968) · Zbl 0165.22305
[5] Herskovits, E.H.; Cooper, G.F., Kutató: an entropy-driven system for the construction of probabilistic expert systems from data, (), 54-62
[6] Cooper, G.; Herskovitz, E., A Bayesian method for the induction of probabilistic networks from data, Machine learning, 9, 320-347, (1992)
[7] De Campos, L.M.; Huete, J.F., Learning non-probabilistic belief networks, ()
[8] Dempster, A.P., Upper and lower probabilities induced by a multivalued mapping, Annals of mathematics and statistics, 38, 315-329, (1967) · Zbl 0168.17501
[9] Drudzel, M.J.; Simon, H.A., Causality in Bayesian belief, (), 3-11
[10] Dubois, D., Belief structures, possibility theory and decomposable confidence measures on finite sets, Computers and artificial intelligence, 5, 5, 403-417, (1986) · Zbl 0657.60006
[11] Dubois, D.; Prade, H., Théorie des possibilités, ()
[12] Dubois, D.; Prade, H., Inference in possibilistic hypergraphs, (), 250-259
[13] Fonck, P., Influence networks in possibility theory, () · Zbl 0976.68525
[14] Fonck, P., Propagating uncertainty in directed acyclic graphs, ()
[15] Fonck, P., Reseaux d’inference pour le raisonnement possibiliste, ()
[16] Fonck, P., Conditional independence in possibility theory, (), 221-226
[17] Fung, R.M.; Crawford, S.L., Constructor: A system for the induction of probabilistic models, (), 762-765
[18] Galles, D.; Pearl, J., Testing identifiability of causal effects, (), 185-195
[19] Galles, D.; Pearl, J., Axioms for causal relevance, () · Zbl 0917.68123
[20] Gebhardt, J.; Kruse, R., The context model: an integrating view of vagueness and uncertainty, International journal of approximate reasoning, 9, 283-314, (1993) · Zbl 0786.68086
[21] Gebhardt, J.; Kruse, R., Learning possibilistic networks from data, () · Zbl 0861.68081
[22] Heckerman, D.A., A Bayesian approach to learning causal networks, ()
[23] Herskovitz, E.H.; Cooper, G., Kutató: an entropy-driven system for the construction of probabilistic expert systems from data, ()
[24] Hisdal, E., Conditional possibilities, independence and non-interaction, Fuzzy sets and systems, 1, 283-297, (1978) · Zbl 0393.94050
[25] Huete, J.F., Aprendizaje de redes de creencia mediante la deteccióm de independencias: modelos no probabilisticos, ()
[26] Huete, J.F.; De Campos, L.M., Learning causal polytrees, ()
[27] Josslyn, C.A., Possibilistic process for complex system modelling, ()
[28] Klir, G.; Folger, T., Fuzzy sets, uncertainty and information, () · Zbl 0675.94025
[29] Lam, W.; Bacchus, F., Using causal information and local measures to learn Bayesian belief networks, (), 243-250
[30] Lam, W.; Bacchus, F., Using new data to refine a Bayesian network, (), 383-390
[31] Murphy, P.M.; Aha, D.W., Uci repository of machine learning databases, machine-readable data repository, (1996), Department of Information and Computer Science, University of California Irvine
[32] Musick, C.R., Belief network induction, ()
[33] Pearl, J., Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988), Morgan Kaufmann San Mateo, CA
[34] Pearl, J., Belief networks revisited, Artificial intelligence, 59, 49-56, (1993)
[35] Pearl, J., Bayesian networks, () · Zbl 0859.68056
[36] Pearl, J.; Paz, A., Graphoids: a graph-based logic for reasoning about relevance relations, ()
[37] Pearl, J.; Verma, T., A theory of inferred causation, () · Zbl 0765.68177
[38] ()
[39] Ramer, A., Conditional possibility measures, Cybernetics and systems, 20, 185-196, (1986)
[40] Rebane, T.; Pearl, J., The recovery of causal poly-trees from statistical data, ()
[41] Sangüesa, R.; Cortés, U., Learning causal networks from data: a survey and a new algorithm for recovering possibilistic causal networks, AI communications, 10, 1-31, (1997)
[42] R. Sangüesa, U. Cortés, J.J. Valdés, M. Poch, I. Roda, Recovering belief networks from data: an application to wastewater treatment plants, Artificial Intelligence in Engineering, submitted.
[43] Sangüesa, R., Learning possibilistic causal networks from data, ()
[44] Shenoy, P.P., Independence in valuation-based systems, () · Zbl 0741.68094
[45] Spirtes, P.; Glymour, C.; Scheines, P., Discovering causal structure, (1987), Springer Berlin
[46] Singh, M.; Valtorta, M., An algorithm for the construction of Bayesian network structures from data, (), 259-265
[47] Singh, M.; Valtorta, M., Construction of Bayesian network structures from data: A survey and an efficient algorithm, International journal of approximate reasoning, 12, 111-131, (1995) · Zbl 0814.68115
[48] Verma, T.; Pearl, J., An algorithm for deciding if a set of observed independencies has a causal explanation, (), 323-330
[49] Zadeh, L., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 12, 1, 3-28, (1978) · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.