Skip to main content

From Information to Evidence in a Bayesian Network

  • Conference paper
Probabilistic Graphical Models (PGM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8754))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)

    Chapter  Google Scholar 

  2. 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)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. Benferhat, S., Tabia, K.: Inference in possibilistic network classifiers under uncertain observations. Annals of Mathematics and Artificial Intelligence 64(2-3), 269–309 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bessière, P., Mazer, E., Ahuactzin, J.M., Mekhnacha, K.: Bayesian Programming. CRC Press (2013)

    Google Scholar 

  6. Bilmes, J.: On soft evidence in Bayesian networks. Tech. Rep. UWEETR-2004-00016, Department of Electrical Engineering University of Washington, Seattle (2004)

    Google Scholar 

  7. Birtles, N., Fenton, N., Neil, M., Tranham, E.: Agenarisk, http://www.agenarisk.com/

  8. Bloemeke, M.: Agent encapsulated Bayesian networks. Ph.d. thesis, Department of Computer Science, University of South Carolina (1998)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. Chan, H.: Sensitivity Analysis of Probabilistic Graphical Models. Ph.d. thesis, University of California, Los Angeles (2005)

    Google Scholar 

  11. Chan, H., Darwiche, A.: Sensitivity analysis in Bayesian networks: From single to multiple parameters. In: UAI, pp. 67–75 (2004)

    Google Scholar 

  12. Chan, H., Darwiche, A.: On the revision of probabilistic beliefs using uncertain evidence. Artificial Intelligence 163(1), 67–90 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. D’Ambrosio, B., Takikawa, M., Upper, D.: Representation for dynamic situation modeling. Technical report, Information Extraction and Transport, Inc. (2000)

    Google Scholar 

  14. Darwiche, A.: Samlam, http://reasoning.cs.ucla.edu/samiam

  15. Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press (2009)

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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)

    Article  MathSciNet  Google Scholar 

  18. Druzdzel, M.J.: Genie smile, http://genie.sis.pitt.edu

  19. 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)

    Google Scholar 

  20. Elvira: Elvira project, http://leo.ugr.es/elvira/

  21. Henrion, M.: Analytica, lumina decision systems, http://www.lumina.com/

  22. Højsgaard, S.: gRain, http://people.math.aau.dk/~sorenh/software/gR/

  23. Jeffrey, R.C.: The Logic of Decision, 2nd edn. 246 pages. University of Chicago Press (1990)

    Google Scholar 

  24. Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs, 2nd edn. Springer Publishing Company, Incorporated (2007)

    Google Scholar 

  25. Jiroušek, R.: Solution of the marginal problem and decomposable distributions. Kybernetika 27, 403–412 (1991)

    MathSciNet  MATH  Google Scholar 

  26. Jouffe, L., Munteanu, P.: Bayesialab, http://www.bayesia.com

  27. Kim, Y.G., Valtorta, M., Vomlel, J.: A prototypical system for soft evidential update. Applied Intelligence 21(1), 81–97 (2004)

    Article  MATH  Google Scholar 

  28. 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)

    Google Scholar 

  29. Korb, K., Nicholson, A.: Bayesian Artificial Intelligence, 2nd edn. Chapman and Hall (2010)

    Google Scholar 

  30. Koski, T., Noble, J.: Bayesian Networks: An Introduction. Wiley Series in Probability and Statistics. Wiley (2009)

    Google Scholar 

  31. 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)

    Google Scholar 

  32. Kruithof, R.: Telefoonverkeersrekening. De Ingenieur 52, 15–25 (1937)

    Google Scholar 

  33. 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)

    Chapter  Google Scholar 

  34. 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)

    Google Scholar 

  35. Lauritzen, S.L.: Hugin, http://www.hugin.com

  36. 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)

    MathSciNet  MATH  Google Scholar 

  37. 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)

    Article  MathSciNet  MATH  Google Scholar 

  38. Minka, T., Winn, J.: Infer.net, http://research.microsoft.com/en-us/um/cambridge/projects/infernet/default.aspx

  39. Murphy, K.: Bayesian network toolbox (bnt), http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html

  40. Naïm, P., Wuillemin, P.H., Leray, P., Pourret, O., Becker, A.: Réseaux bayésiens. Eyrolles, 3 edn. (2007)

    Google Scholar 

  41. Norsys: Netica application (1998), http://www.norsys.com

  42. Pan, R., Peng, Y., Ding, Z.: Belief update in Bayesian networks using uncertain evidence. In: ICTAI, pp. 441–444 (2006)

    Google Scholar 

  43. Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)

    Google Scholar 

  44. 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)

    Article  MathSciNet  MATH  Google Scholar 

  45. 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)

    Article  MathSciNet  MATH  Google Scholar 

  46. Sandiford, J.: Bayes server, http://www.bayesserver.com/

  47. Tomaso, E.D., Baldwin, J.F.: An approach to hybrid probabilistic models. International Journal of Approximate Reasoning 47(2), 202–218 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  48. Valtorta, M., Kim, Y.G., Vomlel, J.: Soft evidential update for probabilistic multiagent systems. International Journal of Approximate Reasoning 29(1), 71–106 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  49. 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)

    Google Scholar 

  50. 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)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics