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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baioletti, M., Busanello, G., Vantaggi, B.: Acyclic directed graphs representing independence models. Int. J. of App. Reas. 52(1), 2–18 (2011)
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)
Clemen, R.T., Fischer, G.W., Winkler, R.L.: Assessing dependence: Some experimental results. Man. Sci. 46(8), 1100–1115 (2000)
Cooke, R.M., Goossens, L.H.J.: TU Delft expert judgment database. Rel. Eng. & Sys. Saf. 93(5), 657–674 (2008)
Dawid, A.P.: Conditional independence in statistical theory. J. of the Royal Stat. Soc. B 41, 15–31 (1979)
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)
Henrion, M., Breese, J.S., Horvitz, E.J.: Decision analysis and expert systems. AI Mag. 12(4), 64–91 (1991)
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)
del Sagrado, J., Moral, S.: Qualitative Combination of Bayesian Networks. Int. J. of Int. Sys. 18, 237–249 (2003)
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)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, Los Altos (1988)
Peña, J.M.: Finding Consensus Bayesian Network Structures. J. of Art. Int. Res. 42, 661–687 (2011)
Studeny, M.: Semigraphoids and structures of probabilistic conditional independence. Ann. of Math. and Art. Int. 21, 71–98 (1997)
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)
Xiang, Y.: Verification of DAG Structures in Cooperative Belief Network-Based Multi-agent Systems. Net. 31, 183–191 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)