In this paper, we propose a method for robust kernel density estimation. We interpret a KDE with Gaussian kernel as the inner product between a mapped test point and the centroid of mapped training points in kernel feature space. Our robust KDE replaces the centroid with a robust estimate based on M-estimation [1]. The iteratively re-weighted least squares (IRWLS) algorithm for M-estimation depends only on inner products, and can therefore be implemented using the kernel trick. We prove the IRWLS method monotonically decreases its objective value at every iteration for a broad class of robust loss functions. Our proposed method is applied to synthetic data and network traffic volumes, and the results compare favorably to the standard KDE. Index Termskernel density estimation, M-estimator, outlier, kernel feature space, kernel trick
A robust kernel density estimator was proposed in REF , by viewing the standard KDE as a mean in a function space, and estimating the mean robustly.
Robust kernel density estimation
2008 IEEE International Conference on Acoustics, Speech and Signal Processing
2008 IEEE International Conference on Acoustics, Speech and Signal Processing
Mathematics Computer Science