Adversarial Meta-Learning of Gamma-Minimax Estimators That Leverage Prior Knowledge

TL;DR

This paper introduces a novel adversarial meta-learning approach to compute Gamma-minimax estimators for general models, enabling incorporation of vague prior knowledge through generalized moments, with applications in entropy estimation and biodiversity prediction.

Contribution

It extends Gamma-minimax estimation to non-parametric models using adversarial meta-learning and neural networks, providing convergence guarantees and practical algorithms.

Findings

Effective estimation in entropy and biodiversity prediction tasks.

The proposed method converges with theoretical guarantees.

Neural network class enhances estimator flexibility.

Abstract

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 $\Gamma$ 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.