Open Access
2023 Adversarial meta-learning of Gamma-minimax estimators that leverage prior knowledge
Hongxiang Qiu, Alex Luedtke
Author Affiliations +
Electron. J. Statist. 17(2): 1996-2043 (2023). DOI: 10.1214/23-EJS2151


Bayes estimators are well known to provide a means to incorporate prior knowledge that can be expressed in terms of a single prior distribution. However, when this knowledge is too vague to express with a single prior, an alternative approach is needed. Gamma-minimax estimators provide such an approach. These estimators minimize the worst-case Bayes risk over a set Γ of prior distributions that are compatible with the available knowledge. Traditionally, Gamma-minimaxity is defined for parametric models. In this work, we define Gamma-minimax estimators for general models and propose adversarial meta-learning algorithms to compute them when the set of prior distributions is constrained by generalized moments. Accompanying convergence guarantees are also provided. We also introduce a neural network class that provides a rich, but finite-dimensional, class of estimators from which a Gamma-minimax estimator can be selected. We illustrate our method in two settings, namely entropy estimation and a prediction problem that arises in biodiversity studies.

Funding Statement

Generous support was provided by Amazon through an AWS Machine Learning Research Award, the NIH under award number DP2-LM013340, and the NSF under award number DMS-2210216. The content is solely the responsibility of the authors and does not necessarily represent the official views of Amazon, the NIH, or the NSF.


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Hongxiang Qiu. Alex Luedtke. "Adversarial meta-learning of Gamma-minimax estimators that leverage prior knowledge." Electron. J. Statist. 17 (2) 1996 - 2043, 2023.


Received: 1 October 2022; Published: 2023
First available in Project Euclid: 3 September 2023

MathSciNet: MR4636234
Digital Object Identifier: 10.1214/23-EJS2151

Keywords: Gamma-minimax estimation , machine learning

Vol.17 • No. 2 • 2023
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