论文标题
具有限制功能的非参数的非参数置信带和带带有paley-fiener的内核
Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions
论文作者
论文摘要
本文介绍了一种基于输入输出对的有限样本的有限带限制功能构建置信带的方法。该方法是免费的W.R.T.假定观察噪声，并且仅假定输入分布的知识。它是非参数，也就是说，它不需要回归函数的参数模型，并且区域具有非反应保证。该算法基于paley-fiener的理论，再现了内核希尔伯特空间。本文首先研究了完全可观察到的变体，当观测值没有噪音并且只有输入是随机的。然后，它使用梯度扰动方法将思想推广到嘈杂的情况下。最后，提出了证明两种情况的数值实验。
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.
