Core Determining Class and Inequality Selection

The relations between unobserved events and observed outcomes can be characterized by a bipartite graph. We propose an algorithm that explores the structure of the graph to construct the "exact Core Determining Class," i.e., the set of irredudant inequalities. We prove that in general the exact Core Determining Class does not depend on the probability measure of the outcomes but only on the structure of the graph. For more general linear inequalities selection problems, we propose a statistical procedure similar to the Dantzig Selector to select the truly informative constraints. We demonstrate performances of our procedures in Monte-Carlo experiments.