Summary
We investigate the problem of calculating likelihoods in Bayesian networks. This is highly relevant to the issue of explanation in such networks and is in many ways complementary to the MAP approach which searches for the explanation that is most probable given evidence. Likelihoods are also of general statistical interest and can be useful if the value of a particular variable is to be maximized. After looking at the simple case where only parents of nodes are considered in the explanation set, we go on to look at tree-structured networks and then at a general approach for obtaining likelihoods.
This is a preview of subscription content, log in via an institution to check access.
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
Pearl J (1988) Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman, San Mateo
Pearl J (2000) Causality: Models, Reasoning and Inference. Cambridge University Press, Cambridge
Shimony AE (1991) Explanation, irrelevance and statistical independence. In: Proceedings of AAAI, pp. 482–487
Suermondt HJ (1992) Explanation in Bayesian belief networks. Ph.D thesis, Stanford University
Henrion M, Druzdzel MJ (1990) Qualitative propagation and scenario-based approaches to explanation of probabilistic reasoning. In: Proceedings of the 6th Conference on Uncertainty in AI, pp. 17–32
Chajewska U, Halpern JY (1997) Defining explanation in probabilistic systems. In: Proceedings of the 13th Conference on Uncertainty in AI, pp. 62–71
Halpern JY, Pearl J (2001) Causes and Explanations: a Structural-Model Approach – Part I: Causes. In: Proceedings of the 17th Conference on Uncertainty in AI, pp. 194–202
Halpern JY, Pearl J (2001) Causes and Explanations: A Structural-Model Approach – Part II: Explanations. Proceedings of the 17th International Joint Conference on AI, pp. 27–34
Salmon WC (1998) Causality and Explanation. Oxford University Press, Oxford
Glass DH (2002) Coherence, explanation and Bayesian networks. In: Proceedings of the 13th Irish Conference on AI and Cognitive Science. Lecture notes in AI 2464:177–182
Jensen FV (1996) An Introduction to Bayesian Networks. UCL Press, London
Neapolitan RE (1990) Probabilistic Reasoning in Expert Systems. Wiley, New York
Cowell RG, Dawid AP, Lauritzen SL, Spiegelhalter DJ (1998) Probabilistic Networks and Expert Systems. Springer, Berlin Heidelberg New York
Lauritzen SL, Spiegelhalter DJ (1988) Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society: Series B 50(2): 157–224
Xu H (1995) Computing marginals for arbitrary subsets from marginal representation in Markov trees. Artificial Intelligence 74:177–189
Nilsson D (1998) An efficient algorithm for finding the M most probable configurations in Bayesian networks. Statistics and Computing 2:159–173
Dawid AP (1992) Applications of a general propagation algorithm for probabilistic expert systems. Statistics and Computing 2:25–36
de Campos LM, Gamez JA, Moral S (2002) On the problem of performing exact partial abductive inferences in Bayesian belief networks using junction trees. Studies in Fuzziness and Soft Computing, 90:289–302
Cooper G (2002) Computation complexity of probabilistic inference using Bayesian belief network. SIAM Journal of Computing 42:393–405
de Campos LM, Gamez JA, Moral S (1999) Partial abductive inference in Bayesian belief networks using a genetic algorithm. Pattern Recognition Letter 20:1211–1217
Park JD, Darwiche A (2001) Approximating MAP using local search. In: Proceedings of the 17th Conference on Uncertainty in AI, pp. 403–410
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Glass, D.H. (2008). Likelihoods and Explanations in Bayesian Networks. In: Chountas, P., Petrounias, I., Kacprzyk, J. (eds) Intelligent Techniques and Tools for Novel System Architectures. Studies in Computational Intelligence, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77623-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-77623-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77621-5
Online ISBN: 978-3-540-77623-9
eBook Packages: EngineeringEngineering (R0)