Bayesian Averaging is Well-Temperated

Lars Kai Hansen

AbstractBayesian predictions are stochastic just like predictions of any other
inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is less clear if the teacher distribution is unknown. I define a class of averaging procedures, the temperated likelihoods, including both Bayes averaging with a uniform prior and maximum likelihood estimation as special cases. I show that
Bayes is generalization optimal in this family for any teacher distribution for two learning problems that are analytically tractable learning the mean of a Gaussian and asymptotics of smooth learners.
TypeConference paper [With referee]
ConferenceAdvances in Neural Information Processing Systems 1999
EditorsS. Solla et al.
Year2000    pp. 265-271
PublisherMIT Press
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing