Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means

Fuente: arXiv
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Autori principali: Høgsgaard, Mikael Møller, Paudice, Andrea
Natura: Preprint
Pubblicazione: 2025
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author Høgsgaard, Mikael Møller
Paudice, Andrea
author_facet Høgsgaard, Mikael Møller
Paudice, Andrea
contents The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class $\mathcal{F}$ when the data distribution possesses only the first $p$ moments for $p \in (1,2]$. We prove a new sample complexity bound using a novel symmetrization technique that may be of independent interest. Additionally, we present applications of our result to $k$-means clustering with unbounded inputs and linear regression with general losses, improving upon existing works.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14673
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
Høgsgaard, Mikael Møller
Paudice, Andrea
Machine Learning
The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class $\mathcal{F}$ when the data distribution possesses only the first $p$ moments for $p \in (1,2]$. We prove a new sample complexity bound using a novel symmetrization technique that may be of independent interest. Additionally, we present applications of our result to $k$-means clustering with unbounded inputs and linear regression with general losses, improving upon existing works.
title Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
topic Machine Learning
url https://arxiv.org/abs/2506.14673