English(EN) Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance

新研究分析了高斯混合模型在Hellinger距离下的NPMLE

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-22 04:00

研究人员分析了用于估计单变量高斯混合密度的非参数最大似然估计量（NPMLE）。他们证明了当混合测度为亚高斯测度时，无约束NPMLE在Hellinger距离平方误差下达到了$\log(n)/n$的minimax最优率。此外，对于具有紧支撑的混合测度，约束在紧区间内的NPMLE也达到了略快的minimax最优率。 AI

影响为与机器学习相关的统计估计方法提供了理论基础。

排序理由学术论文，详细介绍了估计方法的理论分析。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.LG TIER_1 English(EN) · Shayan Hundrieser, Tudor Manole · 2026-10-22 04:00

高斯混合模型在Hellinger距离下NPMLE的Minimax最优性

arXiv:2610.30109v1 Announce Type: cross 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 N…

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高斯混合模型在Hellinger距离下NPMLE的Minimax最优性

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