GRIBONVAL, Rémi; BLANCHARD, Gilles; KERIVEN, Nicolas; TRAONMILIN, Yann

doi:10.4171/msl/21

Métadonnées

Licence d’utilisation du document

GRIBONVAL, Rémi
Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio [PANAMA]
Dynamic Networks : Temporal and Structural Capture Approach [DANTE]

BLANCHARD, Gilles
Laboratoire de Mathématiques d'Orsay [LMO]
Understanding the Shape of Data [DATASHAPE]

KERIVEN, Nicolas
GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes [GIPSA-GAIA]

Langue

Article de revue

Ce document a été publié dans

Mathematical Statistics and Learning. 2021-08-21, vol. 3, n° 2, p. 165–257

EMS Publishing House

Résumé en anglais

We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for compressive clustering and compressive Gaussian mixture modeling with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.< Réduire

Mots clés en anglais

random moments

random features

clustering

mixture modeling

principal component analysis.

principal component analysis

dimension reduction

unsupervised learning

kernel mean embedding

statistical learning

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191510

DOI

http://dx.doi.org/10.4171/msl/21

Projet Européen

PLEASE: Projections, Learning, and Sparsity for Efficient data-processing

Project ANR

Approches statistiquement et computationnellement efficicaces pour l'intelligence artificielle - ANR-19-CHIA-0021
Algorithmes, Approximations, Parcimonie et Plongements pour l'IA - ANR-19-CHIA-0009

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251