Ellipsoid approximation using random vectors

Authors:
S. Mendelson;A. Pajor
Affiliations:
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT, Australia;Equipe d'Analyse et Mathématiques Appliquées, Université de Marne-la-Vallée, Marne-la-Vallée Cedex 2, France
Venue:
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Year:
2005

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Abstract

We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on ${\mathbb R}^{n}$ or on ℓ2. We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectrum of the integral operator.