Estimation consistency of the group lasso and its applications

Han Liu, Jian Zhang

Research output: Contribution to journalConference article

25 Scopus citations

Abstract

We extend the ℓ 2-consistency result of (Meinshausen and Yu 2008) from the Lasso to the group Lasso. Our main theorem shows that the group Lasso achieves estimation consistency under a mild condition and an asymptotic upper bound on the number of selected variables can be obtained. As a result, we can apply the nonnegative garrote procedure to the group Lasso result to obtain an estimator which is simultaneously estimation and variable selection consistent. In particular, our setting allows both the number of groups and the number of variables per group increase and thus is applicable to high-dimensional problems. We also provide estimation consistency analysis for a version of the sparse additive models with increasing dimensions. Some finite-sample results are also reported.

Original languageEnglish (US)
Pages (from-to)376-383
Number of pages8
JournalJournal of Machine Learning Research
Volume5
StatePublished - Dec 1 2009
Event12th International Conference on Artificial Intelligence and Statistics, AISTATS 2009 - Clearwater, FL, United States
Duration: Apr 16 2009Apr 18 2009

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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