On Open Problems Associated with Conditioning in the Dempster-Shafer Belief Function Theory

0576517 - ÚTIA 2024 RIV JP eng C - Konferenční příspěvek (zahraniční konf.)
Jiroušek, Radim - Kratochvíl, Václav - Shenoy, P. P.
On Open Problems Associated with Conditioning in the Dempster-Shafer Belief Function Theory.
Proceedings of the 23rd Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty. Osaka, Japan: Osaka Metropolitan University, 2023 - (Yoshifumi, K.; Václav, K.; Masahiro, I.; Ondřej, Č.), s. 1-10
[Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty 20232 /23./. Matsuyama (JP), 16.09.2023-20.09.2023]
Grant CEP: GA ČR(CZ) GA21-07494S
Institucionální podpora: RVO:67985556
Klíčová slova: belief functions * conditioning * composition * conditional independence
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2023/MTR/kratochvil-0576517.pdf

As in probability theory, graphical and compositional models in the Dempster-Shafer (D-S) belief function theory handle multidimensional belief functions applied to support inference for practical problems. Both types of models represent multidimensional belief functions using their low-dimensional marginals. In the case of graphical models, these marginals are usually conditionals, for compositional models, they are unconditional. Nevertheless, one must introduce some conditioning to compose unconditional belief functions and avoid double-counting knowledge. Thus, conditioning is crucial in processing multidimensional compositional models for belief functions.

This paper summarizes some important open problems, the solution of which should enable a trouble-free design of computational processes employing D-S belief functions in AI. For some of them, we discuss possible solutions. The problems considered in this paper are of two types. There are still some gaps that should be filled to get a mathematically consistent uncertainty theory. Other problems concern the computational tractability of procedures arising from the super-exponential growth of the space and time complexity of the designed algorithms.
Trvalý link: https://hdl.handle.net/11104/0346458