针对重尾分布，提出统一均值估计新方法，提升稳定性与精度。
Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
- 采用新的对称化技术分析中位数均值在重尾数据中的表现
- 在仅存在1到2阶矩条件下，实现更优的样本复杂度
- 适用于无界输入的k-means聚类和广义损失线性回归
中位数均值（Median of Means, MoM）是一种在重尾数据中广受关注的均值估计方法。本文研究在数据分布仅具有1至2阶矩（p ∈ (1,2]）时，同时估计函数类ℱ中每个函数的均值问题。通过引入一种新颖的对称化技术，证明了新的样本复杂度界，该技术本身可能具有独立价值。此外，将结果应用于具有无界输入的k-means聚类和一般损失下的线性回归，改进了现有工作。
原文摘要 · Abstract (English)
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.
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