A Discrete RKHS Standpoint for Nyström MMD - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

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.
Fichier principal
Vignette du fichier
Nyström_MMD_A_Discrete_RKHS_Standpoint.pdf (688.41 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03651849 , version 1 (26-04-2022)

Identifiants

  • HAL Id : hal-03651849 , version 1

Citer

Farah Cherfaoui, Hachem Kadri, Sandrine Anthoine, Liva Ralaivola. A Discrete RKHS Standpoint for Nyström MMD. 2022. ⟨hal-03651849⟩
213 Consultations
189 Téléchargements

Partager

Gmail Facebook X LinkedIn More