Sparse additive models

Pradeep Ravikumar, John Lafferty, Han Liu, Larry Wasserman

Research output: Contribution to journalArticle

232 Scopus citations

Abstract

We present a new class of methods for high dimensional non-parametric regression and classification called sparse additive models. Our methods combine ideas from sparse linear modelling and additive non-parametric regression. We derive an algorithm for fitting the models that is practical and effective even when the number of covariates is larger than the sample size. Sparse additive models are essentially a functional version of the grouped lasso of Yuan and Lin. They are also closely related to the COSSO model of Lin and Zhang but decouple smoothing and sparsity, enabling the use of arbitrary non-parametric smoothers. We give an analysis of the theoretical properties of sparse additive models and present empirical results on synthetic and real data, showing that they can be effective in fitting sparse non-parametric models in high dimensional data.

Original languageEnglish (US)
Pages (from-to)1009-1030
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume71
Issue number5
DOIs
StatePublished - Nov 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Additive models
  • Lasso
  • Non-parametric regression
  • Sparsity

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