论文标题
均值均值原则的强大内核密度估计
Robust Kernel Density Estimation with Median-of-Means principle
论文作者
论文摘要
在本文中，我们介绍了一个结合流行的内核密度估计方法和中位数原理（MOM-KDE）的强大非参数密度估计器。即使在对抗性污染的情况下，该估计器也显示出对任何异常数据的鲁棒性。特别是，尽管以前的作品仅在已知的污染模型下证明了一致性结果，但此工作提供了有限的高概率误差限制，而没有对异常值的先验知识。最后，与其他强大的内核估计器相比，我们表明MOM-KDE取得了竞争性的结果，同时具有明显的计算复杂性。
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.
