Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911013070176256 |
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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 |