Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance

Paper recorded by Signals 4 on 2026-10-21 in cs.LG. Abstract reproduced from arXiv; link to the original below.

Published 2026-10-21 on arXiv · recorded by Signals 4 on 2026-10-22

Category: cs.LG · 机器学习 · first seen 2026-10-22

Abstract

We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples. We show that the unconstrained NPMLE achieves the minimax optimal rate $\log(n)/n$ in squared Hellinger distance, when the true mixing measure is sub-Gaussian. In addition, we show that when the true mi

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