Abstract
Evidence in a Bayesian network comes from information based on the observation of one or more variables. A review of the terminology leads to the assessment that two main types of non-deterministic evidence have been defined, namely likelihood evidence and probabilistic evidence but the distinction between fixed probabilistic evidence and not fixed probabilistic evidence is not clear, and neither terminology nor concepts have been clearly defined. In particular, the term soft evidence is confusing. The article presents definitions and concepts related to the use of non-deterministic evidence in Bayesian networks, in terms of specification and propagation. Several examples help to understand how an initial piece of information can be specified as a finding in a Bayesian network.
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
Ben Mrad, A., Delcroix, V., Maalej, M.A., Piechowiak, S., Abid, M.: Uncertain evidence in Bayesian networks: Presentation and comparison on a simple example. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 39–48. Springer, Heidelberg (2012)
Ben Mrad, A., Maalej, M.A., Delcroix, V., Piechowiak, S., Abid, M.: Fuzzy evidence in Bayesian networks. In: Proc. of Soft Computing and Pattern Recognition, Dalian, China (2011)
Ben Mrad, A., Delcroix, V., Piechowiak, S., Maalej, M.A., Abid, M.: Understanding soft evidence as probabilistic evidence: Illustration with several use cases. In: 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), pp. 1–6 (2013)
Benferhat, S., Tabia, K.: Inference in possibilistic network classifiers under uncertain observations. Annals of Mathematics and Artificial Intelligence 64(2-3), 269–309 (2012)
Bessière, P., Mazer, E., Ahuactzin, J.M., Mekhnacha, K.: Bayesian Programming. CRC Press (2013)
Bilmes, J.: On soft evidence in Bayesian networks. Tech. Rep. UWEETR-2004-00016, Department of Electrical Engineering University of Washington, Seattle (2004)
Birtles, N., Fenton, N., Neil, M., Tranham, E.: Agenarisk, http://www.agenarisk.com/
Bloemeke, M.: Agent encapsulated Bayesian networks. Ph.d. thesis, Department of Computer Science, University of South Carolina (1998)
Butz, C.J., Fang, F.: Incorporating evidence in Bayesian networks with the select operator. In: Kégl, B., Lee, H.-H. (eds.) AI 2005. LNCS (LNAI), vol. 3501, pp. 297–301. Springer, Heidelberg (2005)
Chan, H.: Sensitivity Analysis of Probabilistic Graphical Models. Ph.d. thesis, University of California, Los Angeles (2005)
Chan, H., Darwiche, A.: Sensitivity analysis in Bayesian networks: From single to multiple parameters. In: UAI, pp. 67–75 (2004)
Chan, H., Darwiche, A.: On the revision of probabilistic beliefs using uncertain evidence. Artificial Intelligence 163(1), 67–90 (2005)
D’Ambrosio, B., Takikawa, M., Upper, D.: Representation for dynamic situation modeling. Technical report, Information Extraction and Transport, Inc. (2000)
Darwiche, A.: Samlam, http://reasoning.cs.ucla.edu/samiam
Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press (2009)
Delcroix, V., Sedki, K., Lepoutre, F.X.: A Bayesian network for recurrent multi-criteria and multi-attribute decision problems: Choosing a manual wheelchair. Expert Systems with Applications 40(7), 2541–2551 (2013)
Deming, W.E., Stephan, F.F.: On a least square adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics 11, 427–444 (1940)
Druzdzel, M.J.: Genie smile, http://genie.sis.pitt.edu
Dubois, D., Moral, S., Prade, H.: Belief change rules in ordinal and numerical uncertainty theories. In: Gabbay, D., Smets, P. (eds.) Belief Change, (D. Dubois, H. Prade, eds.). Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3, pp. 311–392. Kluwer Academic Publishers, Dordrecht (1998)
Elvira: Elvira project, http://leo.ugr.es/elvira/
Henrion, M.: Analytica, lumina decision systems, http://www.lumina.com/
Højsgaard, S.: gRain, http://people.math.aau.dk/~sorenh/software/gR/
Jeffrey, R.C.: The Logic of Decision, 2nd edn. 246 pages. University of Chicago Press (1990)
Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs, 2nd edn. Springer Publishing Company, Incorporated (2007)
Jiroušek, R.: Solution of the marginal problem and decomposable distributions. Kybernetika 27, 403–412 (1991)
Jouffe, L., Munteanu, P.: Bayesialab, http://www.bayesia.com
Kim, Y.G., Valtorta, M., Vomlel, J.: A prototypical system for soft evidential update. Applied Intelligence 21(1), 81–97 (2004)
Kjaerulff, U., Madsen, A.: Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Information science and statistics, 2nd edn., vol. 22. Springer (2013)
Korb, K., Nicholson, A.: Bayesian Artificial Intelligence, 2nd edn. Chapman and Hall (2010)
Koski, T., Noble, J.: Bayesian Networks: An Introduction. Wiley Series in Probability and Statistics. Wiley (2009)
Krieg, M.L.: A tutorial on Bayesian belief networks. Tech. Rep. DSTO-TN-0403, Surveillance Systems Division, Electronics and Surveillance Research Laboratory, Defense science and technology organisation, Edinburgh, South Australia, Australia (2001)
Kruithof, R.: Telefoonverkeersrekening. De Ingenieur 52, 15–25 (1937)
Langevin, S., Valtorta, M.: Performance evaluation of algorithms for soft evidential update in Bayesian networks: First results. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 284–297. Springer, Heidelberg (2008)
Langevin, S., Valtorta, M., Bloemeke, M.: Agent-encapsulated Bayesian networks and the rumor problem. In: AAMAS 2010 Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 1553–1554 (2010)
Lauritzen, S.L.: Hugin, http://www.hugin.com
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, Series B 50, 157–224 (1988)
Madsen, A.L., Jensen, F.V.: Lazy propagation: A junction tree inference algorithm based on lazy evaluation. Artificial Intelligence 113(1-2), 203–245 (1999)
Minka, T., Winn, J.: Infer.net, http://research.microsoft.com/en-us/um/cambridge/projects/infernet/default.aspx
Murphy, K.: Bayesian network toolbox (bnt), http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html
Naïm, P., Wuillemin, P.H., Leray, P., Pourret, O., Becker, A.: Réseaux bayésiens. Eyrolles, 3 edn. (2007)
Norsys: Netica application (1998), http://www.norsys.com
Pan, R., Peng, Y., Ding, Z.: Belief update in Bayesian networks using uncertain evidence. In: ICTAI, pp. 441–444 (2006)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)
Peng, Y., Zhang, S., Pan, R.: Bayesian network reasoning with uncertain evidences. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18(5), 539–564 (2010)
Peng, Y., Ding, Z., Zhang, S., Pan, R.: Bayesian network revision with probabilistic constraints. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20(3), 317–337 (2012)
Sandiford, J.: Bayes server, http://www.bayesserver.com/
Tomaso, E.D., Baldwin, J.F.: An approach to hybrid probabilistic models. International Journal of Approximate Reasoning 47(2), 202–218 (2008)
Valtorta, M., Kim, Y.G., Vomlel, J.: Soft evidential update for probabilistic multiagent systems. International Journal of Approximate Reasoning 29(1), 71–106 (2002)
Vomlel, J.: Probabilistic reasoning with uncertain evidence. Neural Network World, International Journal on Neural and Mass-Parallel Computing and Information Systems 14(5), 453–465 (2004)
Zhang, S., Peng, Y., Wang, X.: An Efficient Method for Probabilistic Knowledge Integration. In: Proceedings of the 20th IEEE International Conference on Tools with Artificial Intelligence. IEEE Computer Society (November 2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ben Mrad, A., Delcroix, V., Piechowiak, S., Leicester, P. (2014). From Information to Evidence in a Bayesian Network. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-11433-0_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11432-3
Online ISBN: 978-3-319-11433-0
eBook Packages: Computer ScienceComputer Science (R0)