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Title: On the conditional independence implication problem: A lattice-theoretic approach
Authors: Niepert, Mathias 
Gyssens, Marc 
Sayrafi, Bassem 
Van Gucht, Dirk 
Keywords: Computer adaptive testing;Conditional independence;Probabilities;Mathematical statistics;Computer science - Mathematics;Lattice theory;Engineering mathematics
Issue Date: 2013
Publisher: Artificial Intelligence
Abstract: A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a finite, sound and complete inference system relative to semilattice inclusions is presented. This system is shown to be (1) sound and complete for saturated CI statements, (2) complete for general CI statements, and (3) sound and complete for stable CI statements. These results yield a criterion that can be used to falsify instances of the implication problem and several heuristics are derived that approximate this “lattice exclusion” criterion in polynomial time. Finally, we provide experimental results that relate our work to results obtained from other existing inference algorithms.
DOI: 10.1016/j.artint.2013.06.005
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