ICML 2025poster0 citations
The Empirical Mean is Minimax Optimal for Local Glivenko-Cantelli
Doron Cohen, Aryeh Kontorovich, Roi Weiss
Abstract
We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convergence rates of the Empirical Mean Estimator (EME). In this work, we investigate generalizations of this setting where arbitrary estimators are allowed rather than just the EME. Can a strictly larger class of measures be learned? Can better risk decay rates be obtained? We provide exhaustive answers to these questions—which are both negative, provided the learner is barred from exploiting some infinite-dimensional pathologies. On the other hand, allowing such exploits does lead to a strictly larger class of learnable measures.
Maximum Likelihood EstimatorLocal Glivenko-CantelliSymmetryStatistical EstimationMinimaxMachine Learning
BibTeX
@inproceedings{
cohen2025the,
title={The Empirical Mean is Minimax Optimal for Local Glivenko-Cantelli},
author={Doron Cohen and Aryeh Kontorovich and Roi Weiss},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=36oullXtuS}
}