Uncertainty-Aware Bayes' Rule and Its Applications

원문 초록

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.