Oberwolfach Reports


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Volume 6, Issue 1, 2009, pp. 867–916
DOI: 10.4171/OWR/2009/16

Published online: 2009-12-23

Sparse Recovery Problems in High Dimensions: Statistical Inference and Learning Theory

Peter L. Bartlett[1], Vladimir Koltchinskii[2], Alexandre B. Tsybakov[3] and Sara van de Geer[4]

(1) University of California, Berkeley, USA
(2) Georgia Institute of Technology, Atlanta, USA
(3) CREST, Malakoff, France
(4) ETH Zentrum, Z├╝rich, Switzerland

The statistical analysis of high dimensional data requires new techniques, extending results from nonparametric statistics, analysis, probability, approximation theory, and theoretical computer science. The main problem is how to unveil, (or to mimic performance of) sparse models for the data. Sparsity is generally meant in terms of the number of variables included, but may also be described in terms of smoothness, entropy, or geometric structures. A key objective is to adapt to unknown sparsity, yet keeping computational feasibility.

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Bartlett Peter, Koltchinskii Vladimir, Tsybakov Alexandre, van de Geer Sara: Sparse Recovery Problems in High Dimensions: Statistical Inference and Learning Theory. Oberwolfach Rep. 6 (2009), 867-916. doi: 10.4171/OWR/2009/16