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Inference in Credal Networks with BranchAndBound Algorithms
 IN INT. SYMP. ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
, 2003
"... A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree mo ..."
Abstract

Cited by 11 (1 self)
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A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree models. We describe
Separation Properties of Sets of Probability Measures
 In Conference on Uncertainty in Artificial Intelligence
, 2000
"... This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparati ..."
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Cited by 5 (1 self)
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This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparation but still fails to guarantee a belief separation property. To overcome this unsatisfactory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this result implies that (1) separation properties of Bayesian networks do extend to epistemic independence and sets of probability measures, and (2) strong independence has a clear justi cation based on epistemic independence and the strong Markov condition. 1