Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition
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Abstract (arXiv)
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high dimensional problems. In the it sparse regime when the components are sufficiently smooth or the dimensionality is sufficiently large, the optimal rates are identical to those for high dimensional linear regression, and therefore there is no additional cost to entertain a nonparametric model. Otherwise, in the so-called it smooth regime, the rates coincide with the optimal rates for estimating a univariate function, and therefore they are immune to the "curse of dimensionality".
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2015.
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Citing papers per year: 2021: 2; 2022: 1; 2023: 2; 2024: 4; 2025: 1; 2026: 3.
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- 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimensioncited by 15
- 2021Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectivescited by 12
- 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learningcited by 7
- 2021Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactionscited by 3
- 2024Gradient Descent Finds Over-Parameterized Neural Networks with Sharp Generalization for Nonparametric Regressioncited by 2
- 2024Distributed Learning with Discretely Observed Functional Datacited by 1
- 2024Generalized Sparse Additive Model with Unknown Link Functioncited by 1
- 2022DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelationcited by 0
- 2023Minimax Signal Detection in Sparse Additive Modelscited by 0
- 2025Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Feature Learning by Learnable Channel Attentioncited by 0
- 2026Statistical Inference for Explainable Boosting Machinescited by 0
- 2026Gradient Descent with Projection Finds Over-Parameterized Neural Networks for Learning Low-Degree Polynomials with Nearly Minimax Optimal Ratecited by 0
1 more
- 2026Minimax Additive Regression under Unknown Dependent Designs30 Sep 2026
- 2026Gradient Descent with Projection Finds Over-Parameterized Neural Networks for Learning Low-Degree Polynomials with Nearly Minimax Optimal Rate22 Mar 2026
- 2026Statistical Inference for Explainable Boosting Machines26 Jan 2026
- 2025Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Feature Learning by Learnable Channel Attention23 Dec 2025
- 2024Gradient Descent Finds Over-Parameterized Neural Networks with Sharp Generalization for Nonparametric Regression5 Nov 2024
- 2024Generalized Sparse Additive Model with Unknown Link Function8 Oct 2024
- 2024Distributed Learning with Discretely Observed Functional Data3 Oct 2024
- 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning7 May 2024
- 2023Minimax Signal Detection in Sparse Additive Models19 Apr 2023
- 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension12 Feb 2023
- 2022DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation16 May 2022
- 2021Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactions24 Aug 2021
- 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimensioncited by 15
- 2021Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectivescited by 12
- 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learningcited by 7
- 2021Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactionscited by 3
- 2024Gradient Descent Finds Over-Parameterized Neural Networks with Sharp Generalization for Nonparametric Regressioncited by 2
- 2024Distributed Learning with Discretely Observed Functional Datacited by 1
- 2024Generalized Sparse Additive Model with Unknown Link Functioncited by 1
- 2022DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelationcited by 0
- 2023Minimax Signal Detection in Sparse Additive Modelscited by 0
- 2025Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Feature Learning by Learnable Channel Attentioncited by 0
- 2026Statistical Inference for Explainable Boosting Machinescited by 0
- 2026Gradient Descent with Projection Finds Over-Parameterized Neural Networks for Learning Low-Degree Polynomials with Nearly Minimax Optimal Ratecited by 0
12 most cited of 13 All 13 (JSON)
- 2026Minimax Additive Regression under Unknown Dependent Designs30 Sep 2026
- 2026Gradient Descent with Projection Finds Over-Parameterized Neural Networks for Learning Low-Degree Polynomials with Nearly Minimax Optimal Rate22 Mar 2026
- 2026Statistical Inference for Explainable Boosting Machines26 Jan 2026
- 2025Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Feature Learning by Learnable Channel Attention23 Dec 2025
- 2024Gradient Descent Finds Over-Parameterized Neural Networks with Sharp Generalization for Nonparametric Regression5 Nov 2024
- 2024Generalized Sparse Additive Model with Unknown Link Function8 Oct 2024
- 2024Distributed Learning with Discretely Observed Functional Data3 Oct 2024
- 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning7 May 2024
- 2023Minimax Signal Detection in Sparse Additive Models19 Apr 2023
- 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension12 Feb 2023
- 2022DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation16 May 2022
- 2021Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactions24 Aug 2021
12 newest of 13 All 13 (JSON)