Spectral Regularization for Support Estimation

In this paper we consider the problem of learning from data the support of a prob-ability distribution when the distribution does not have a density (with respect to some reference measure). We propose a new class of regularized spectral esti-mators based on a new notion of reproducing kernel Hilbert space, which we call “completely regular”. Completely regular kernels allow to capture the relevant geometric and topological properties of an arbitrary probability space. In partic-ular, they are the key ingredient to prove the universal consistency of the spectral estimators and in this respect they are the analogue of universal kernels for su-pervised problems. Numerical experiments show that spectral estimators compare favorably to state of the art machine learning algorithms for density support esti-mation.