提出适用于非高斯噪声的核回归统一误差界，提升安全关键场景下的不确定性量化精度。
On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise
- 基于核回归构建非渐近概率误差界，支持多种非高斯噪声分布
- 在相关与独立噪声下均有效，误差界更紧致，覆盖范围更广
- 适合对不确定性敏感的安全控制等关键应用
在安全关键领域，从带噪观测中获得函数估计的非保守不确定性量化仍是一个基本挑战。本文提出了核回归的新型非渐近概率统一误差界。相较于文献中仅限于（条件）独立子高斯噪声的边界，本方法可处理广泛的非高斯分布，包括子高斯、有界、子指数及方差/矩有界的噪声。此外，结果适用于相关与不相关噪声。通过比较所提误差界与现有方法在诱导不确定性区域和安全控制中的表现，验证了其紧致性与优越性。
原文摘要 · Abstract (English)
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this work, we propose novel non-asymptotic probabilistic uniform error bounds for kernel-based regression. Compared to related bounds in the literature that are restricted to (conditionally) independent sub-Gaussian noise, our bounds allow to consider a broad class of non-Gaussian distributions, such as sub-Gaussian, bounded, sub-exponential, and variance/moment-bounded noise. Moreover, our results apply to correlated and uncorrelated noise. We compare our proposed error bounds with existing results in terms of the induced uncertainty region and their performance in safe control, demonstrating the tightness of the proposed bounds.
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