PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Sparsity oracle inequalities for the Lasso.
Florentina Bunea, Alexandre Tsybakov and Marten Wegkamp
Electronic Journal of Statistics Volume 1, pp. 169-194, 2007.


This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. They can be applied to high-dimensional linear regression, to nonparametric adaptive regression estimation and to the problem of aggregation of arbitrary estimators.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3861
Deposited By:Alexandre Tsybakov
Deposited On:25 February 2008