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Citation link: https://media.suub.uni-bremen.de/handle/elib/6416
 
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A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence


Authors: Goldenbaum, Mario  
Dytso, Alex  
Poor, H. Vincent  
Shamai Shitz, Shlomo  
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.
Keywords: Bregman Divergence
Issue Date: 2022
Publisher: PMLR
Journal/Edited collection: Proceedings of Machine Learning Research 
Start page: 8080
End page: 8094
Band: 151
Type: Artikel/Aufsatz
ISSN: 2640-3498
Institution: Hochschule Bremen 
Faculty: Hochschule Bremen - Fakultät 4: Elektrotechnik und Informatik 
Appears in Collections:Bibliographie HS Bremen

  

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