# Improving Kernel-Based Nonasymptotic Simultaneous Confidence Bands

arXiv: https://arxiv.org/abs/2401.15791 · HTML: https://mlsanity.com/paper/2401.15791/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 28 Jan 2024.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models](https://mlsanity.com/paper/1807.08216/) (2018)
- [Distribution-Free Uncertainty Quantification for Kernel Methods by Gradient Perturbations](https://mlsanity.com/paper/1812.09632/) (2018)
- [Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions](https://mlsanity.com/paper/2206.13629/) (2022)
- [Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets](https://mlsanity.com/paper/1412.2352/) (2014)

## Built on by (most cited first, 4 of 4)

- [Derandomizing Simultaneous Confidence Regions for Band-Limited Functions by Improved Norm Bounds and Majority-Voting Schemes](https://mlsanity.com/paper/2506.17764/) (2025)
- [Single Image Inpainting and Super-Resolution with Simultaneous Uncertainty Guarantees by Universal Reproducing Kernels](https://mlsanity.com/paper/2506.23221/) (2025)
- [Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases](https://mlsanity.com/paper/2507.06657/) (2025)
- [MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra](https://mlsanity.com/paper/2609.09436/) (2026)

## Abstract (arXiv)

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of the paper is a recently developed algorithm to which we propose three types of improvements. First, we relax the assumptions on the noises by replacing the symmetricity assumption with a weaker distributional invariance principle. Then, we propose a more efficient way to estimate the norm of the target function, and finally we enhance the construction of the confidence bands by tightening the constraints of the underlying convex optimization problems. The refinements are also illustrated through numerical experiments.