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Preprints, Working Papers, ... Year : 2024

Support and distribution inference from noisy data

Abstract

Understanding what kind of noise in the observations allow to recover low dimensional structures of a signal is of interest in statistical learning, as a first step to build efficient dimension reduction procedures. In this work we give a new contribution on the type of noise which can affect the data without preventing to build consistent estimators of the support and distribution of the signal. We focus on the situation where the observations are corrupted with additive and independent noise. We prove that for general classes of supports, it is possible to recover both the support and the distribution of the signal without knowing the noise distribution and with no sample of the noise. We exhibit classes of distributions over which we prove adaptive minimax rates (up to a \log \log factor) for the estimation of the support in Hausdorff distance. Moreover, for the class of distributions with compact support, we provide estimators of the unknown (in general singular) distribution and prove maximum rates in Wasserstein distance. We also prove an almost matching lower bound on the associated minimax risk.
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Dates and versions

hal-04073724 , version 1 (19-04-2023)
hal-04073724 , version 2 (24-05-2024)

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Jeremie Capitao-Miniconi, Élisabeth Gassiat, Luc Lehéricy. Support and distribution inference from noisy data. 2024. ⟨hal-04073724v2⟩
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