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Sparse additive models

Author

Listed:
  • Pradeep Ravikumar
  • John Lafferty
  • Han Liu
  • Larry Wasserman

Abstract

Summary. 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.

Suggested Citation

  • Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:1009-1030
    DOI: 10.1111/j.1467-9868.2009.00718.x
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    References listed on IDEAS

    as
    1. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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