Abstract
We present a method to fuse pieces of probabilistic information stemming from different sources which is based on information theoretical optimization techniques. We use the well-known principle of maximum entropy to process information most faithfully, while interactions between the different knowledge bases are precluded. The so-defined fusion operator satisfies basic demands, such as commutativity and the Pareto principle. A detailed analysis shows it to merge the corresponding epistemic states. Furthermore, it induces a numerical fusion operator that computes the information theoretical mean of probabilities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alchourrón, C., Gärdenfors, P., Makinson, P.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)
Bloch, I., Hunter, A., et al.: Fusion: General concepts and characteristics. International Journal of Intelligent Systems 16, 1107–1134 (2001)
Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 263–294 (1991)
Konieczny, S., Pino-Perez, R.: On the logic of merging. In: Proceedings Sixth International Conference on Principles of Knowledge Representation and Reasoning, KR 1998, pp. 488–498 (1998)
Maynard-Reid II, P., Lehmann, D.: Representing and aggregating conflicting beliefs. In: Proceedings Seventh International Conference on Principles of Knowledge Representation and Reasoning, KR 2000 (2000)
Dubois, D., Lang, J., Prade, H.: Dealing with multi-source information in possibilistic logic. In: Proceedings ECAI 1992, pp. 38–42 (1992)
Schramm, M., Ertel, W.: (PIT), www.pit-systems.de
Rödder, W., Meyer, C.H.: (SPIRIT), www.fernuni-hagen.de/BWLOR/forsch.html
Rödder, W., Meyer, C.H.: Coherent knowledge processing at maximum entropy by SPIRIT. In: Horvitz, E., Jensen, F. (eds.) Proceedings 12th Conference on Uncertainty in Artificial Intelligence, San Francisco, Ca., pp. 470–476. Morgan Kaufmann, San Francisco (1996)
Schramm, M., Ertel, W.: Reasoning with probabilities and maximum entropy: the system PIT and its application in LEXMED. In: Symposium on Operations Research, SOR 1999 (1999)
Cowell, R., Dawid, A., Lauritzen, S., Spiegelhalter, D.: Probabilistic networks and expert systems. Springer, Heidelberg (1999)
Jaynes, E.: Where do we stand on maximum entropy? In: Papers on Probability, Statistics and Statistical Physics, pp. 210–314. D. Reidel Publishing Company, Dordrecht (1983)
Shore, J., Johnson, R.: Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transactions on Information Theory IT-26, 26–37 (1980)
Paris, J., Vencovská, A.: A note on the inevitability of maximum entropy. International Journal of Approximate Reasoning 14, 183–223 (1990)
Kern-Isberner, G.: Characterizing the principle of minimum cross-entropy within a conditional-logical framework. Artificial Intelligence 98, 169–208 (1998)
Kern-Isberner, G.: The principle of conditional preservation in belief revision. In: Eiter, T., Schewe, K.-D. (eds.) FoIKS 2002. LNCS, vol. 2284, pp. 105–129. Springer, Heidelberg (2002)
Kern-Isberner, G.: Handling conditionals adequately in uncertain reasoning and belief revision. Journal of Applied Non-Classical Logics 12, 215–237 (2002)
Rödder, W., Kern-Isberner, G.: From information to probability: an axiomatic approach. International Journal of Intelligent Systems 18, 383–403 (2003)
Rödder, W., Xu, L.: Entropy-driven inference and inconsistency. In: Proceedings Artificial Intelligence and Statistics, Fort Lauderdale, Florida, pp. 272–277 (1999)
Csiszár, I.: I-divergence geometry of probability distributions and minimization problems. Ann. Prob. 3, 146–158 (1975)
Paris, J.: The uncertain reasoner’s companion – A mathematical perspective. Cambridge University Press, Cambridge (1994)
Kern-Isberner, G.: Conditionals in nonmonotonic reasoning and belief revision. In: Kern-Isberner, G. (ed.) Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)
Sen, A.: Social choice theory. In: Arrow, K., Intriligator, M. (eds.) Handbook of Mathematical Economics, vol. III, pp. 1073–1181. Elsevier Science Publishers, Amsterdam (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kern-Isberner, G., Rödder, W. (2003). Fusing Probabilistic Information on Maximum Entropy. In: Günter, A., Kruse, R., Neumann, B. (eds) KI 2003: Advances in Artificial Intelligence. KI 2003. Lecture Notes in Computer Science(), vol 2821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39451-8_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-39451-8_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20059-8
Online ISBN: 978-3-540-39451-8
eBook Packages: Springer Book Archive