提出一种紧致的多输出核回归不确定性界，适用于有界噪声。
Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function
- 基于对偶方法构建无约束确定性边界
- 在有界噪声下实现比现有方法更紧的不确定性估计
- 结构与经典高斯过程置信区间一致，易融入优化流程
从含噪声数据中可靠预测隐函数所需的非保守不确定性界是实现安全学习控制的关键。核方法如高斯过程回归因其内在的不确定性量化机制而成为主流，但现有方法或对噪声分布假设过强，或过于保守，无法直接应用于多输出情形，或难以集成到下游任务中。本文通过无约束对偶公式，为有界噪声下再生核希尔伯特空间（RKHS）中的多输出函数提出了一个紧致的确定性边界。该边界结构与经典的高斯过程置信区间一致，可直接嵌入下游优化流程。我们证明了所提边界能推广已有结果，并通过仿真实例展示其在四旋翼动力学学习中的应用。
原文摘要 · Abstract (English)
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality-based formulation, which shares the same structure as classic Gaussian process confidence bounds, and can thus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。