Isolation Kernel Estimators

Existing adaptive kernel density estimators (KDEs) and kernel regressions (KRs) often employ a data-independent kernel, such as Gaussian kernel. They require an additional means to adapt the kernel bandwidth locally in a given dataset in order to produce better estimations. But this comes with high computational cost. In this paper, we show that adaptive KDEs and KRs can be directly derived from Isolation Kernel with constant-time complexity for each estimation. The resultant estimators called IKDE and IKR are the first KDE and KR that are fast and adaptive. We demonstrate both the superior efficiency and efficacy of IKDE and IKR in anomaly detection and regression tasks, respectively.