Robust Kernel Density Estimation
Abstract
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical -estimation. We interpret the KDE based on a radial, positive semi-definite kernel as a sample mean in the associated reproducing kernel Hilbert space. Since the sample mean is sensitive to outliers, we estimate it robustly via -estimation, yielding a robust kernel density estimator (RKDE). An RKDE can be computed efficiently via a kernelized iteratively re-weighted least squares (IRWLS) algorithm. Necessary and sufficient conditions are given for kernelized IRWLS to converge to the global minimizer of the -estimator objective function. The robustness of the RKDE is demonstrated with a representer theorem, the influence function, and experimental results for density estimation and anomaly detection.
Cite
@article{arxiv.1107.3133,
title = {Robust Kernel Density Estimation},
author = {JooSeuk Kim and Clayton D. Scott},
journal= {arXiv preprint arXiv:1107.3133},
year = {2011}
}