Constructing consonant predictive beliefs from data with scenario theory

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de Angelis, Marco and Rocchetta, Roberto and Gray, Ander and Ferson, Scott (2021) Constructing consonant predictive beliefs from data with scenario theory. Proceedings of Machine Learning Research, 147. pp. 357-360. ISSN 2640-3498

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Abstract

A method for constructing consonant predictive beliefs for multivariate datasets is presented. We make use of recent results in scenario theory to construct a family of enclosing sets that are associated with a predictive lower probability of new data falling in each given set. We show that the sequence of lower bounds indexed by enclosing set yields a consonant belief function. The presented method does not rely on the construction of a likelihood function, therefore possibility distributions can be obtained without the need for normalization. We present a practical example in two dimensions for the sake of visualization, to demonstrate the practical procedure of obtaining the sequence of nested sets.

ORCID iDs

de Angelis, Marco ORCID logoORCID: https://orcid.org/0000-0001-8851-023X, Rocchetta, Roberto, Gray, Ander and Ferson, Scott;
CORE (COnnecting REpositories)