In this paper we introduce a novel method that can efficiently estimate a family of hierarchical dense sets in high-dimensional distributions. Our method can be regarded as a natural extension of the one-class SVM (OCSVM) algorithm that finds multiple parallel separating hyperplanes in a reproducing kernel Hilbert space. We call our method q-OCSVM, as it can be used to estimate $q$ quantiles of a high-dimensional distribution. For this purpose, we introduce a new global convex optimization program that finds all estimated sets at once and show that it can be solved efficiently. We prove the correctness of our method and present empirical results that demonstrate its superiority over existing methods.

We propose an efficient, generalized, nonparametric, statistical Kolmogorov-Smirnov test for detecting distributional change in high-dimensional data. To implement the test, we introduce a novel, hierarchical, minimum-volume sets estimator to represent the distributions to be tested. Our work is motivated by the need to detect changes in data streams, and the test is especially efficient in this context. We provide the theoretical foundations of our test and show its superiority over existing methods.