The paper introduces a method to construct confidence bands for bounded, band-limited functions based on a finite sample of input-output pairs. The approach is distribution-free w.r.t. the observation noises and only the knowledge of the input distribution is assumed. It is nonparametric, that is, it does not require a parametric model of the regression function and the regions have non-asymptotic guarantees. The algorithm is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. The paper first studies the fully observable variant, when there are no noises on the observations and only the inputs are random; then it generalizes the ideas to the noisy case using gradient-perturbation methods. Finally, numerical experiments demonstrating both cases are presented.
翻译:本文采用了一种方法,根据输入-产出对子的有限样本,为捆绑、带限制的功能构建信任带。 这种方法是无分布式的观测噪音,只假设对输入分布的了解。 它不是参数, 也就是说, 它不需要回归函数的参数模型, 区域有非无损保证。 算法基于 Paley- Wiener 复制内核Hilbert 空间的理论。 论文首先研究了完全可观测的变量, 当观测时没有噪音, 只有输入是随机的; 然后它用梯度- 扰动方法将想法概括到吵闹的个案中。 最后, 提供了数字实验, 展示了这两个案例。