From probability theory we know the concepts of stochastic independence and conditional independence of random variables. These notions capture the presence or absence of influence of the information on certain variables on other ones. These influence structures are both important for modeling and for computation. As may be conjectured, such questions of mutual influence of variables over other ones are not confined to the formalism of probability theory, but are more general (see for example (Cowell et. al., 1999; Studeny, 1993)). In particular the notion of conditional independence can be introduced at the level of valuation algebras, generalizing thus the notion of stochastic independence of random variables. This has already been noted in (Shenoy, 1997 a). Conditional independence regarded from the point of view of valuation algebras will be the subject of the present chapter.
KeywordsUndirected Graph Conditional Independence Markov Property Positive Element Factor Graph
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