Qualitative Combination of Independence Models

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.

[1]  S. Destercke E. Chojnacki.  Handling dependencies between variables with imprecise probabilistic models , 2008 .

[2]  Yang Xiang.  Verification of DAG structures in cooperative belief network‐based multiagent systems , 1998 .

[3]  Cory J. Butz,et al.  Constructing the Dependency Structure of a Multiagent Probabilistic Network , 2001, IEEE Trans. Knowl. Data Eng..

[4]  Bruce Abramson,et al.  Some Complexity Considerations in the Combination of Belief Networks , 1993, UAI.

[6]  Simon Parsons,et al.  An application of formal argumentation: Fusing Bayesian networks in multi-agent systems , 2007, Artif. Intell..

[7]  Barbara Vantaggi,et al.  Acyclic directed graphs representing independence models , 2011, Int. J. Approx. Reason..

[8]  Serafín Moral,et al.  Qualitative combination of Bayesian networks , 2003, Int. J. Intell. Syst..

[9]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[10]  José M. Peña,et al.  Finding Consensus Bayesian Network Structures , 2011, J. Artif. Intell. Res..

[11]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[12]  Roger M. Cooke,et al.  TU Delft expert judgment data base , 2008, Reliab. Eng. Syst. Saf..

[13]  Robert L. Winkler,et al.  Assessing Dependence: Some Experimental Results , 2000 .

[14]  Milan Studený,et al.  Semigraphoids and structures of probabilistic conditional independence , 1997, Annals of Mathematics and Artificial Intelligence.

[15]  Barbara Vantaggi,et al.  Conditional independence structure and its closure: Inferential rules and algorithms , 2009, Int. J. Approx. Reason..

[16]  Eric Horvitz,et al.  Decision Analysis and Expert Systems , 1991, AI Mag..