A Monte-Carlo Algorithm for Dempster-Shafer Belief
Nic Wilson
TL;DR
This paper introduces a computationally efficient Monte-Carlo algorithm for calculating Dempster-Shafer belief, significantly reducing complexity and enabling broader applications in belief function calculations.
Contribution
The paper presents a novel Monte-Carlo algorithm that computes Dempster-Shafer belief in linear time, improving efficiency over existing methods and extending applicability to other logics.
Findings
Bel calculation time is linear in the size of the subset and belief functions
Algorithm improves complexity of Shenoy-Shafer algorithms on Markov trees
Method can be generalized to other logics for belief calculation
Abstract
A very computationally-efficient Monte-Carlo algorithm for the calculation of Dempster-Shafer belief is described. If Bel is the combination using Dempster's Rule of belief functions Bel, ..., Bel,7, then, for subset b of the frame C), Bel(b) can be calculated in time linear in 1(31 and m (given that the weight of conflict is bounded). The algorithm can also be used to improve the complexity of the Shenoy-Shafer algorithms on Markov trees, and be generalised to calculate Dempster-Shafer Belief over other logics.
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Logic, Reasoning, and Knowledge · AI-based Problem Solving and Planning