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 66 articles , 1 standard article )

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  1. Huet, Sylvie; Taupin, Marie-Luce: Metamodel construction for sensitivity analysis (2017)
  2. Lv, Shaogao; He, Xin; Wang, Junhui: A unified penalized method for sparse additive quantile models: an RKHS approach (2017)
  3. Reese, Timothy; Mojirsheibani, Majid: On the $L_p$ norms of kernel regression estimators for incomplete data with applications to classification (2017)
  4. Scornet, Erwan: Tuning parameters in random forests (2017)
  5. Amato, Umberto; Antoniadis, Anestis; De Feis, Italia: Additive model selection (2016)
  6. Biau, Gérard; Fischer, Aurélie; Guedj, Benjamin; Malley, James D.: COBRA: a combined regression strategy (2016)
  7. Christmann, Andreas; Zhou, Ding-Xuan: Learning rates for the risk of kernel-based quantile regression estimators in additive models (2016)
  8. Ginsbourger, David; Roustant, Olivier; Durrande, Nicolas: On degeneracy and invariances of random fields paths with applications in Gaussian process modelling (2016)
  9. Goia, Aldo (ed.); Vieu, Philippe (ed.): An introduction to recent advances in high/infinite dimensional statistics (2016)
  10. Kwemou, Marius: Non-asymptotic oracle inequalities for the Lasso and group Lasso in high dimensional logistic model (2016)
  11. Shah, Rajen D.: Modelling interactions in high-dimensional data with backtracking (2016)
  12. Zhang, Yichi; Staicu, Ana-Maria; Maity, Arnab: Testing for additivity in non-parametric regression (2016)
  13. Fan, Yingying; James, Gareth M.; Radchenko, Peter: Functional additive regression (2015)
  14. Hu, Yuao; Zhao, Kaifeng; Lian, Heng: Bayesian quantile regression for partially linear additive models (2015)
  15. Klopp, Olga; Pensky, Marianna: Sparse high-dimensional varying coefficient model: nonasymptotic minimax study (2015)
  16. Liu, JingYuan; Zhong, Wei; Li, RunZe: A selective overview of feature screening for ultrahigh-dimensional data (2015)
  17. Ma, Shujie; Carroll, Raymond J.; Liang, Hua; Xu, Shizhong: Estimation and inference in generalized additive coefficient models for nonlinear interactions with high-dimensional covariates (2015)
  18. Ni, Yang; Stingo, Francesco C.; Baladandayuthapani, Veerabhadran: Bayesian nonlinear model selection for gene regulatory networks (2015)
  19. Radchenko, Peter: High dimensional single index models (2015)
  20. Yang, Yun; Tokdar, Surya T.: Minimax-optimal nonparametric regression in high dimensions (2015)

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