On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise
It provides more general and tighter uncertainty quantification for kernel regression, which is crucial for safety-critical applications like safe control.
This paper proposes novel non-asymptotic probabilistic uniform error bounds for kernel regression that apply to a broad class of non-Gaussian noise distributions, including sub-Gaussian, bounded, sub-exponential, and variance/moment-bounded noise, as well as correlated noise. The bounds are shown to be tighter than existing results in safe control applications.
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.