On deviation probabilities in non-parametric regression with heavy-tailed noise

Anna Ben-Hamou; Arnaud Guyader

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arXiv · 2301.10498

On deviation probabilities in non-parametric regression with heavy-tailed noise

Anna Ben-Hamou·Arnaud Guyader

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Abstract

This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression function is Lipschitz, and the noise is only assumed to have a finite second moment. We first specify the fundamental limits of the problem by establishing a general lower bound on deviation probabilities, and then construct explicit estimators that achieve this bound. These estimators are obtained by applying the median-of-means principle to classical local averaging rules in non-parametric regression, including nearest neighbors and kernel procedures.

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Anna Ben-Hamou, Arnaud Guyader. 2023-01-25. On deviation probabilities in non-parametric regression with heavy-tailed noise. https://arxiv.org/abs/2301.10498

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