We provide uniform confidence bands for kernel ridge regression (KRR), with finite sample guarantees. KRR is ubiquitous, yet--to our knowledge--this paper supplies the first exact, uniform confidence bands for KRR in the non-parametric regime where the regularization parameter $\lambda$ converges to 0, for general data distributions. Our proposed uniform confidence band is based on a new, symmetrized multiplier bootstrap procedure with a closed form solution, which allows for valid uncertainty quantification without assumptions on the bias. To justify the procedure, we derive non-asymptotic, uniform Gaussian and bootstrap couplings for partial sums in a reproducing kernel Hilbert space (RKHS) with bounded kernel. Our results imply strong approximation for empirical processes indexed by the RKHS unit ball, with sharp, logarithmic dependence on the covering number.

翻译：我们为内核脊回归(KRR)提供统一的信任带,并有有限的样本保证。KRR是无处不在的,但对我们的知识来说,本文提供了在非参数制度中KRR在非参数体系中的第一个精确的统一信任带,因为常规数据分布的正规化参数$\lambda$趋同为0。我们提议的统一信任带是基于一个新的、对称化的增殖靴套件程序,采用封闭式解决方案,允许在不假定偏差的情况下进行有效的不确定性量化。为了证明这一程序的合理性,我们从一个再生产内核的Hilbert空间(RKHS)中获取部分数量的非无障碍、统一的高斯和靴套式组合。我们的结果意味着对由RKHS单位球指数化的经验过程的强烈近似性,对覆盖数字有强烈的逻辑依赖。