Adversarial meta-learning of Gamma-minimax estimators that leverage prior knowledge.
Electron J Stat
; 17(2): 1996-2043, 2023.
Article
em En
| MEDLINE
| ID: mdl-38463692
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 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.
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01-internacional
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MEDLINE
Idioma:
En
Ano de publicação:
2023
Tipo de documento:
Article