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Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

Author

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  • Ray Bai
  • Gemma E. Moran
  • Joseph L. Antonelli
  • Yong Chen
  • Mary R. Boland

Abstract

Abstract–We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and automatic self-adaptivity to different levels of sparsity. We develop theory to uniquely characterize the global posterior mode under the SSGL and introduce a highly efficient block coordinate ascent algorithm for maximum a posteriori estimation. We further employ de-biasing methods to provide uncertainty quantification of our estimates. Thus, implementation of our model avoids the computational intensiveness of Markov chain Monte Carlo in high dimensions. We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through extensive simulations and data analysis. Supplementary materials for this article are available online.

Suggested Citation

  • Ray Bai & Gemma E. Moran & Joseph L. Antonelli & Yong Chen & Mary R. Boland, 2022. "Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 184-197, January.
  • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:537:p:184-197
    DOI: 10.1080/01621459.2020.1765784
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    Cited by:

    1. Pereira, Luz Adriana & Gutiérrez, Luis & Taylor-Rodríguez, Daniel & Mena, Ramsés H., 2023. "Bayesian nonparametric hypothesis testing for longitudinal data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    2. Haofeng Wang & Hongxia Jin & Xuejun Jiang & Jingzhi Li, 2022. "Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation," Mathematics, MDPI, vol. 10(23), pages 1-22, December.

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