Skip to main content

Qualitative Combination of Independence Models

  • Conference paper
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013)

Abstract

We deal with the problem of combining sets of independence statements coming from different experts. It is known that the independence model induced by a strictly positive probability distribution has a graphoid structure, but the explicit computation and storage of the closure (w.r.t. graphoid properties) of a set of independence statements is a computational hard problem. For this, we rely on a compact symbolic representation of the closure called fast closure and study three different combination strategies of two sets of independence statements, working on fast closures. We investigate when the complete DAG representability of the given models is preserved in the combined one.

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. Baioletti, M., Busanello, G., Vantaggi, B.: Acyclic directed graphs representing independence models. Int. J. of App. Reas. 52(1), 2–18 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baioletti, M., Busanello, G., Vantaggi, B.: Conditional independence structure and its closure: Inferential rules and algorithms. Int. J. of App. Reas. 50, 1097–1114 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Clemen, R.T., Fischer, G.W., Winkler, R.L.: Assessing dependence: Some experimental results. Man. Sci. 46(8), 1100–1115 (2000)

    Article  MATH  Google Scholar 

  4. Cooke, R.M., Goossens, L.H.J.: TU Delft expert judgment database. Rel. Eng. & Sys. Saf. 93(5), 657–674 (2008)

    Article  Google Scholar 

  5. Dawid, A.P.: Conditional independence in statistical theory. J. of the Royal Stat. Soc. B 41, 15–31 (1979)

    Google Scholar 

  6. Destercke, S., Chojnacki, E.: Handling dependencies between variables with imprecise probabilistic models. Saf., Rel. and Risk An.: Th., Meth. and App. 1-4, 697–702 (2009)

    Google Scholar 

  7. Henrion, M., Breese, J.S., Horvitz, E.J.: Decision analysis and expert systems. AI Mag. 12(4), 64–91 (1991)

    Google Scholar 

  8. Nielsen, S.H., Parsons, S.: An application of formal argumentation: Fusing Bayesian networks in multi-agent systems. Art. Int. 171(10-15), 754–775 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. del Sagrado, J., Moral, S.: Qualitative Combination of Bayesian Networks. Int. J. of Int. Sys. 18, 237–249 (2003)

    Article  MATH  Google Scholar 

  10. Matzkevich, I., Abramson, B.: Some complexity considerations in the combination of belief networks. In: Proc. 9th Conf. UAI, pp. 159–165. Morgan Kaufmann, San Francisco (1993)

    Google Scholar 

  11. Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, Los Altos (1988)

    Google Scholar 

  12. Peña, J.M.: Finding Consensus Bayesian Network Structures. J. of Art. Int. Res. 42, 661–687 (2011)

    MATH  Google Scholar 

  13. Studeny, M.: Semigraphoids and structures of probabilistic conditional independence. Ann. of Math. and Art. Int. 21, 71–98 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wong, S.K.M., Butz, C.J.: Constructing the Dependency Structure of a Multiagent Probabilistic Network. IEEE Trans. on Knowl. and Data Eng. 13(3), 395–415 (2001)

    Article  Google Scholar 

  15. Xiang, Y.: Verification of DAG Structures in Cooperative Belief Network-Based Multi-agent Systems. Net. 31, 183–191 (1998)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baioletti, M., Petturiti, D., Vantaggi, B. (2013). Qualitative Combination of Independence Models. In: van der Gaag, L.C. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2013. Lecture Notes in Computer Science(), vol 7958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39091-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39091-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39090-6

  • Online ISBN: 978-3-642-39091-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics