Skip to main content
SpringerLink
Log in

Divergence Measures and Approximate Algorithms for Valuation Based Systems

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 855))

  • 1227 Accesses

Abstract

This paper considers an abstract framework for expressing approximate inference algorithms in valuation based systems. It will provide a definition of a ‘more informative’ binary relation between representations of information as well as the basic properties of a divergence measure. The approach is illustrated with the cases of probabilistic reasoning (computation of marginal probabilities and most probable explanation) and with inference problems in propositional logic. Examples of divergence measures satisfying the basic properties will be given for these problems. Finally, we will formulate in an abstract way the mean field variational approach and the iterative belief propagation algorithm.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. Shafer, G., Shenoy, P.: Local computation in hypertrees. Working Paper N. 201, School of Business, University of Kansas, Lawrence (1988)

    Google Scholar 

  2. Shenoy, P., Shafer, G.: Axioms for probability and belief-function propagation. In: Shachter, et al. (ed.) Uncertainty in Artificial Intelligence, vol. 4, pp. 169–198. Elsevier, Amsterdam (1990)

    Chapter  Google Scholar 

  3. Cano, J., Delgado, M., Moral, S.: An axiomatic system for the propagation of uncertainty in directed acyclic networks. Int. J. Approx. Reasoning 8, 253–280 (1993)

    Article  Google Scholar 

  4. Kohlas, J.: Information Algebras: Generic Structures for Inference. Springer, London (2012). https://doi.org/10.1007/978-1-4471-0009-6

    Book  MATH  Google Scholar 

  5. Kohlas, J., Moral, S.: Propositional information systems. Working Paper N. 96–01, Institute of Informatics, University of Fribourg (1996)

    Google Scholar 

  6. Hernández, L., Moral, S.: Mixing exact and importance sampling propagation algorithms in dependence graphs. Int. J. Intell. Syst. 12, 553–576 (1997)

    Article  Google Scholar 

  7. Pearl, J.: Evidential reasoning using stochastic simulation of causal models. Artif. Intell. 32, 247–257 (1987)

    Article  MathSciNet  Google Scholar 

  8. Hernández, L., Moral, S., Salmerón, A.: Importance sampling algorithms in belief networks based on aproximate computation. In: Proceedings of Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference (IPMU 1996), vol. 2, Granada, pp. 859–864 (1996)

    Google Scholar 

  9. Moral, S., Salmerón, A.: Dynamic importance sampling in Bayesian networks based on probability trees. Int. J. Approx. Reasoning 38(3), 245–261 (2005)

    Article  MathSciNet  Google Scholar 

  10. Dechter, R., Rish, I.: Mini-buckets: a general scheme for bounded inference. J. ACM (JACM) 50(2), 107–153 (2003)

    Article  MathSciNet  Google Scholar 

  11. Wainwright, M.J., Jordan, M.I., et al.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1(1–2), 1–305 (2008)

    Article  Google Scholar 

  12. McEliece, R.J., MacKay, D.J.C., Cheng, J.F.: Turbo decoding as an instance of pearl’s “belief propagation” algorithm. IEEE J. Sel. Areas Commun. 16(2), 140–152 (1998)

    Article  Google Scholar 

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

    Book  Google Scholar 

  14. Cano, A., Moral, S., Salmerón, A.: Novel strategies to approximate probability trees in penniless propagation. Int. J. Intell. Syst. 18(2), 193–203 (2003)

    Article  Google Scholar 

  15. Kask, K., Dechter, R.: Branch and bound with mini-bucket heuristics. IJCAI 99, 426–433 (1999)

    Google Scholar 

  16. Kullback, S., Leibler, R.: On information and sufficiency. Ann. Math. Stat. 22, 76–86 (1951)

    Article  MathSciNet  Google Scholar 

  17. Kohlas, J., Wilson, N.: Semiring induced valuation algebras: exact and approximate local computation algorithms. Artif. Intell. 172(11), 1360–1399 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research was supported by the Spanish Ministry of Economy and Competitiveness under project TIN2016-77902-C3-2-P and the European Regional Development Fund (FEDER).

Author information

Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain

    Serafín Moral

Authors
  1. Serafín Moral
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Serafín Moral .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Institute for Research and Applications, University of Ostrava, Ostrava, Czech Republic

    Irina Perfilieva

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Moral, S. (2018). Divergence Measures and Approximate Algorithms for Valuation Based Systems. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91479-4_49

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91478-7

  • Online ISBN: 978-3-319-91479-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation