A Polyhedral Approach to Learning Belief Functions from Imprecise Data
Abstrakt
We address the problem of learning belief functions from empirical data when observations may be imprecise. Our approach is based on the interpretation of belief functions as lower envelopes of sets of probability measures. Empirical data are first transformed into statistically justified lower bounds on event probabilities using confidence intervals. These bounds define a feasible polytope of belief functions compatible with the data. Since this polytope generally contains infinitely many belief functions, we propose to select representative solutions by optimizing linear criteria over the polytope.