2022/02/23 by Alex Dytso, Dytso, Alex, Mario Goldenbaum +5 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST) #cs.LG #math.ST #stat.ME #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.2202.11598
To appear in the proceedings of 25th International Conference on Artificial Intelligence and Statistics (AISTATS) 2022
arxiv created 2022/02/23 · arxiv updated 2022/02/24
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.