A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence

Document Type

Conference Proceeding

Publication Date

1-1-2022

Abstract

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.

Identifier

85163111076 (Scopus)

Publication Title

Proceedings of Machine Learning Research

e-ISSN

26403498

First Page

8080

Last Page

8094

Volume

151

Grant

BSF-2018710

Fund Ref

National Science Foundation

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