2021/07/13 by Maxime Chaveroche, Chaveroche, Maxime, Franck Davoine +3 · 1 citation
Computer Science · #Bayesian Modeling and Causal Inference
paper · pdf · doi:10.48550/arxiv.2107.06329
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory,\noffering useful additional information, but suffers from a high computational\nburden. A lot of work has been done to reduce the complexity of computations\nused in information fusion with Dempster's rule. Yet, few research had been\nconducted to reduce the complexity of computations for the conjunctive and\ndisjunctive decompositions of evidence, which are at the core of other\nimportant methods of information fusion. In this paper, we propose a method\ndesigned to exploit the actual evidence (information) contained in these\ndecompositions in order to compute them. It is based on a new notion that we\ncall focal point, derived from the notion of focal set. With it, we are able to\nreduce these computations up to a linear complexity in the number of focal sets\nin some cases. In a broader perspective, our formulas have the potential to be\ntractable when the size of the frame of discernment exceeds a few dozen\npossible states, contrary to the existing litterature. This article extends\n(and translates) our work published at the french conference GRETSI in 2019.\n