Aggregation and sparsity via ℓ1 penalized least squares

Authors:
Florentina Bunea;Alexandre B. Tsybakov;Marten H. Wegkamp
Affiliations:
Department of Statistics, Florida State University, Tallahassee, FL;Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, PARIS, France;Department of Statistics, Florida State University, Tallahassee, FL
Venue:
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Year:
2006

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Abstract

This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via ℓ1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.