Robust Kernel Density Estimation with Median-of-Means principle

Pierre Humbert, Batiste Le Bars, Ludovic Minvielle
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9444-9465, 2022.

Abstract

In this paper, we introduce a robust non-parametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness for a large class of anomalous data, potentially adversarial. In particular, while previous works only prove consistency results under very specific contamination models, this work provides finite-sample high-probability error-bounds without any prior knowledge on the outliers. To highlight the robustness of our method, we introduce an influence function adapted to the considered OUI framework. Finally, we show that MoM-KDE achieves competitive results when compared with other robust kernel estimators, while having significantly lower computational complexity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-humbert22a, title = {Robust Kernel Density Estimation with Median-of-Means principle}, author = {Humbert, Pierre and Bars, Batiste Le and Minvielle, Ludovic}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {9444--9465}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/humbert22a/humbert22a.pdf}, url = {https://proceedings.mlr.press/v162/humbert22a.html}, abstract = {In this paper, we introduce a robust non-parametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness for a large class of anomalous data, potentially adversarial. In particular, while previous works only prove consistency results under very specific contamination models, this work provides finite-sample high-probability error-bounds without any prior knowledge on the outliers. To highlight the robustness of our method, we introduce an influence function adapted to the considered OUI framework. Finally, we show that MoM-KDE achieves competitive results when compared with other robust kernel estimators, while having significantly lower computational complexity.} }
Endnote
%0 Conference Paper %T Robust Kernel Density Estimation with Median-of-Means principle %A Pierre Humbert %A Batiste Le Bars %A Ludovic Minvielle %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-humbert22a %I PMLR %P 9444--9465 %U https://proceedings.mlr.press/v162/humbert22a.html %V 162 %X In this paper, we introduce a robust non-parametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness for a large class of anomalous data, potentially adversarial. In particular, while previous works only prove consistency results under very specific contamination models, this work provides finite-sample high-probability error-bounds without any prior knowledge on the outliers. To highlight the robustness of our method, we introduce an influence function adapted to the considered OUI framework. Finally, we show that MoM-KDE achieves competitive results when compared with other robust kernel estimators, while having significantly lower computational complexity.
APA
Humbert, P., Bars, B.L. & Minvielle, L.. (2022). Robust Kernel Density Estimation with Median-of-Means principle. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:9444-9465 Available from https://proceedings.mlr.press/v162/humbert22a.html.

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