Entropy for evaluation of Dempster-Shafer belief function models

Abstract

Applications of Dempster-Shafer (D-S) belief functions to practical problems involve difficulties arising from their high computational complexity. One can use space-saving factored approximations such as graphical belief function models to solve them. Using an analogy with probability distributions, we represent these approximations in the form of compositional models. Since no theoretical apparatus similar to probabilistic information theory exists for D-S belief functions (e.g., dissimilarity measure analogous to the Kullback-Liebler divergence measure), the problems arise not only in connection with the design of algorithms seeking optimal approximations but also in connection with a criterion comparing two different approximations. In this respect, the application of the analogy with probability theory fails. Therefore, in this paper, we conduct some synthetic experiments and describe the results designed to reveal whether some belief function entropy definitions described in the literature can detect optimal approximations, i.e., that achieve their minimum for an optimal approximation.