Learning Belief Functions from Data via Polyhedral Methods

Abstrakt

We present a polyhedral framework for learning belief functions from data when empirical lower and upper probability bounds are obtained from Jeffreys’ binomial confidence intervals. Such bounds, interpreted as empirical belief and plausibility values for all subsets of the outcome space, generally yield a pseudo-belief function that may not correspond to any valid basic probability assignment (BPA) satisfying the axioms of Dempster–Shafer theory. Our approach formulates the correction problem as a system of linear constraints in the BPA space, where the feasible solutions form a convex polyhedron of belief functions consistent with the empirical bounds. We investigate several linear optimization criteria for selecting a representative BPA from this feasible set, including L1-projection to the empirical lower bounds, Dubois–Prade entropy maximization, sparsity-oriented objectives, and cardinality-weighted allocations.