JournalsowrVol. 6 , No. 1DOI 10.4171/owr/2009/16

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

  • Sara van de Geer

    ETH Zentrum, Zürich, Switzerland
  • Peter L. Bartlett

    University of California, Berkeley, USA
  • Vladimir Koltchinskii

    Georgia Institute of Technology, Atlanta, USA
  • Alexandre B. Tsybakov

    CREST, Malakoff, France
Sparse Recovery Problems in High Dimensions: Statistical Inference and Learning Theory cover

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Abstract

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.