Derandomizing Simultaneous Confidence Regions for Band-Limited Functions by Improved Norm Bounds and Majority-Voting Schemes
Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for band-limited functions from noisy input-output measurements, by working in a Paley-Wiener reproducing kernel Hilbert space. Kernel norm bounds are tightened using a uniformly-randomized Hoeffding's inequality for small samples and an empirical Bernstein bound for larger ones. We derive an approximate threshold, based on the sample size and how informative the inputs are, that governs which bound to deploy. Finally, we apply majority voting to aggregate confidence sets from random subsamples, boosting both stability and region size. We prove that even per-input aggregated intervals retain their simultaneous coverage guarantee. These refinements are also validated through numerical experiments.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Simultaneous Inference Bands for Autocorrelations
Sample autocorrelograms typically come with significance bands (non-rejection regions) for the null hypothesis of temporal independence. These bands have two shortcomings. First, they build on pointwise intervals and suf…
regressionTime SeriesvalidImproving Kernel-Based Nonasymptotic Simultaneous Confidence Bands
The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based o…
Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions
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…
Bandwidth limited object recognition in high resolution imagery
This paper proposes a novel method to optimize bandwidth usage for object detection in critical communication scenarios. We develop two operating models of active information seeking. The first model identifies promising…
Objectobject-detectionObject DetectionObject Recognition+1Confidence Intervals and Simultaneous Confidence Bands Based on Deep Learning
Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assess…
Deep LearningUncertainty Quantificationvalid