Bayesian Averaging is Well-TemperatedOpen Website

1999 (edited Jul 16, 2019)NIPS 1999Readers: Everyone
  • Abstract: Bayesian 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.
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