A Discrete RKHS Standpoint for Nyström MMD
Résumé
Maximum mean discrepancy (MMD) is a kernelbased distance measure between probability distributions. It relies on the concept of mean embedding of distributions in a Reproducing Kernel Hilbert Space (RKHS). In this work, we describe a new link between probability distributions and kernel methods. We build upon recent and elegant results on RKHSs over discrete domains which possess novel and appealing properties compared to their continuous counterparts. Based on the observation that discrete RKHSs can contain the Dirac masses, we propose a novel framework for representing and comparing probability distributions. We show how MMD and its fast approximation, Nyström MMD, can be retrieved from the discrete RKHS framework. Our results provide an explanation why MMD and Nyström MMD with a large class of kernels, including graph kernels, remains effective in practice. Our approach is empirically illustrated in the context of three-sample testing.
Domaines
Intelligence artificielle [cs.AI]Origine | Fichiers produits par l'(les) auteur(s) |
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