# Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model

arXiv: https://arxiv.org/abs/1503.02978 · HTML: https://mlsanity.com/paper/1503.02978/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2015.

## Built on by (most cited first, 5 of 5)

- [Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques](https://mlsanity.com/paper/2102.09743/) (2021)
- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [Orthogonalized Kernel Debiased Machine Learning for Multimodal Data Analysis](https://mlsanity.com/paper/2103.07088/) (2021)
- [Post-Regularization Confidence Bands for Ordinary Differential Equations](https://mlsanity.com/paper/2110.12510/) (2021)
- [Nonparametric Additive Value Functions: Interpretable Reinforcement Learning with an Application to Surgical Recovery](https://mlsanity.com/paper/2308.13135/) (2023)

## Abstract (arXiv)

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in its own right. Existing methods for fitting sparse additive model are primarily based on sieve estimators, while the literature on confidence bands for nonparametric models are primarily based upon kernel or local polynomial estimators. Our kernel-sieve hybrid estimator combines the best of both worlds and allows us to provide a simple procedure for constructing confidence bands in high-dimensional sparse additive models. We prove that the confidence bands are asymptotically honest by studying approximation with a Gaussian process. Thorough numerical results on both synthetic data and real-world neuroscience data are provided to demonstrate the efficacy of the theory.