Robust Kernel Density Estimation with Median-of-Means principle

Pierre Humbert; Batiste Le Bars; Ludovic Minvielle; Nicolas Vayatis

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arXiv · 2006.16590

Robust Kernel Density Estimation with Median-of-Means principle

Pierre Humbert·Batiste Le Bars·Ludovic Minvielle·Nicolas Vayatis

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Abstract

In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous data, even in the case of adversarial contamination. In particular, while previous works only prove consistency results under known contamination model, this work provides finite-sample high-probability error-bounds without a priori knowledge on the outliers. Finally, when compared with other robust kernel estimators, we show that MoM-KDE achieves competitive results while having significant lower computational complexity.

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BibTeX RIS

Pierre Humbert, Batiste Le Bars, Ludovic Minvielle, Nicolas Vayatis. 2020-06-30. Robust Kernel Density Estimation with Median-of-Means principle. https://arxiv.org/abs/2006.16590

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