Belief Functions: Past, Present, and Future
The theory of belief functions, sometimes referred to as evidence theory or Dempster-Shafer theory, was first introduced by Arthur P. Dempster in the context of statistical inference, to be later developed by Glenn Shafer as a general framework for modelling epistemic uncertainty. Belief theory and the closely related random set theory form a natural framework for modelling situations in which data are missing or scarce: think of extremely rare events such as volcanic eruptions or power plant meltdowns, problems subject to huge uncertainties due to the number and complexity of the factors involved (e.g. climate change), but also the all-important issue with generalisation from small training sets in machine learning.
This short talk abstracted from an upcoming half-day tutorial at IJCAI 2016 is designed to introduce to non-experts the principles and rationale of random sets and belief function theory, review its rationale in the context of frequentist and Bayesian interpretations of probability but also in relationship with the other main approaches to non-additive probability, survey the key elements of the methodology and the most recent developments, discuss current trends in both its theory and applications. Finally, a research program for the future is outlined, which include a robustification of Vapnik' statistical learning theory for an Artificial Intelligence 'in the wild.'