Constructing consonant predictive beliefs from data with scenario theory

Marco de Angelis, Roberto Rocchetta, Ander Gray, Scott Ferson

Research output: Contribution to journalConference Contributionpeer-review

1 Citation (Scopus)
16 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)357-360
Number of pages4
JournalProceedings of Machine Learning Research
Volume147
Publication statusPublished - 16 Jun 2021
Event12th International Symposium on Imprecise Probability: Theories and Applications: Theories and Applications - Granada, Spain
Duration: 6 Jul 20219 Jul 2021

Keywords

  • predictive beliefs
  • consonant random sets
  • generalization error
  • imprecise probability
  • evidence theory

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