Reference
Robust Kernel Density Estimation by Scaling and Projection in Hilbert Space,
Advances in Neural Information Processing Systems(2014)
Abstract
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the
nonparametric setting. We present a robust version of the popular kernel density
estimator (KDE). As with other estimators, a robust version of the KDE is useful
since sample contamination is a common issue with datasets. What “robustness”
means for a nonparametric density estimate is not straightforward and is a topic
we explore in this paper. To construct a robust KDE we scale the traditional KDE
and project it to its nearest weighted KDE in the L
2 norm. This yields a scaled
and projected KDE (SPKDE). Because the squared L
2 norm penalizes point-wise
errors superlinearly this causes the weighted KDE to allocate more weight to high
density regions. We demonstrate the robustness of the SPKDE with numerical
experiments and a consistency result which shows that asymptotically the SPKDE
recovers the uncontaminated density under sufficient conditions on the contamination.