High-dimensional additive modeling. We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.

References in zbMATH (referenced in 51 articles , 1 standard article )

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  1. Biau, Gérard; Fischer, Aurélie; Guedj, Benjamin; Malley, James D.: COBRA: a combined regression strategy (2016)
  2. Christmann, Andreas; Zhou, Ding-Xuan: Learning rates for the risk of kernel-based quantile regression estimators in additive models (2016)
  3. Ginsbourger, David; Roustant, Olivier; Durrande, Nicolas: On degeneracy and invariances of random fields paths with applications in Gaussian process modelling (2016)
  4. Goia, Aldo; Vieu, Philippe: An introduction to recent advances in high/infinite dimensional statistics (2016)
  5. Shah, Rajen D.: Modelling interactions in high-dimensional data with backtracking (2016)
  6. Hu, Yuao; Zhao, Kaifeng; Lian, Heng: Bayesian quantile regression for partially linear additive models (2015)
  7. Liu, JingYuan; Zhong, Wei; Li, RunZe: A selective overview of feature screening for ultrahigh-dimensional data (2015)
  8. Radchenko, Peter: High dimensional single index models (2015)
  9. Bühlmann, Peter; Peters, Jonas; Ernest, Jan: CAM: causal additive models, high-dimensional order search and penalized regression (2014)
  10. Dalalyan, Arnak; Ingster, Yuri; Tsybakov, Alexandre B.: Statistical inference in compound functional models (2014)
  11. Ferraty, Frédéric; Vieu, Philippe: Nonparametric statistics and high/infinite dimensional data (2014)
  12. Huang, Zhensheng; Pang, Zhen; Lin, Bingqing; Shao, Quanxi: Model structure selection in single-index-coefficient regression models (2014)
  13. Jirak, Moritz: Simultaneous confidence bands for sequential autoregressive fitting (2014)
  14. Lian, Heng; Li, Jianbo; Tang, Xingyu: SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part (2014)
  15. Tyagi, Hemant; Cevher, Volkan: Learning non-parametric basis independent models from point queries via low-rank methods (2014)
  16. van de Geer, Sara: Weakly decomposable regularization penalties and structured sparsity (2014)
  17. van de Geer, Sara: On the uniform convergence of empirical norms and inner products, with application to causal inference (2014)
  18. Yoshida, Takuma; Naito, Kanta: Asymptotics for penalised splines in generalised additive models (2014)
  19. Zhang, Shangli; Wang, Lichun; Lian, Heng: Estimation by polynomial splines with variable selection in additive Cox models (2014)
  20. Abramovich, Felix; Grinshtein, Vadim: Estimation of a sparse group of sparse vectors (2013)

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