Robust Kernel Density Estimation with Median-of-Means principle
This work addresses robust density estimation for data analysis in adversarial or contaminated settings, offering an incremental improvement with practical computational benefits.
The paper tackles robust density estimation by combining Kernel Density Estimation with the Median-of-Means principle (MoM-KDE), achieving robustness to adversarial contamination and providing finite-sample error bounds without prior knowledge of outliers. It shows competitive results with significantly lower computational complexity compared to other robust kernel estimators.
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.