Introducing statistical consistency for infinite chance constraints

• Published in: Annals of mathematics and artificial intelligence Vol. 83; no. 2; pp. 165 - 181
• Main Authors: Zghidi, Imen, Hnich, Brahim, Rebai, Abdelwaheb
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2018; Springer; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Complex Systems; Computer Science; Confidence intervals; Consistency; Error correction; Mathematics; Random variables; Statistical analysis; Statistical inference; Statistical consistency; Constraint propagation; 62F25; Infinite chance constraints
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-018-9572-3

In this paper, we propose a novel notion of statistical consistency for single-stage Stochastic Constraint Satisfaction Problems (SCSPs) in which some of the random variables’ support set is infinite. The essence of this novel notion of local consistency is to be able to make an inference in the presence of infinite scenarios in an uncertain environment. This inference would be based on a restricted finite subset of scenarios with a certain confidence level and a threshold tolerance error. The confidence level is the probability that characterizes the extend to which our inference — based on a subset of scenarios — is correct. The threshold tolerance error is the error range that we can tolerate while making such an inference. We propose a novel statistical consistency enforcing algorithm that is based on sound statistical inference; and experimentally show how to prune inconsistent values in the presence of an infinite set of scenarios.