Uncertainty-Aware Bayes' Rule and Its Applications (2311.05532v3)

Abstract: Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule is questionable. Philosophically, the key is to balance the relative importance between prior and data distributions when calculating posterior distributions: if prior distributions are overly conservative (i.e., exceedingly spread), we upweight the prior belief; if prior distributions are overly opportunistic (i.e., exceedingly concentrated), we downweight the prior belief. The same operation also applies to data distributions. This paper studies a generalized Bayes' rule, called uncertainty-aware Bayes' rule, to technically realize the above philosophy, thus combating the model uncertainties in prior and/or data distributions. Applications of the uncertainty-aware Bayes' rule on classification and estimation are discussed: In particular, the uncertainty-aware Bayes classifier, the uncertainty-aware Kalman filter, the uncertainty-aware particle filter, and the uncertainty-aware interactive-multiple-model filter are suggested and experimentally validated.