Spatially-adaptive sensing in nonparametric regression

TL;DR

This paper introduces a spatially adaptive sensing algorithm for nonparametric regression that improves convergence rates for inhomogeneous functions while maintaining uniform design properties.

Contribution

The paper presents a novel adaptive-sensing algorithm applicable to general nonparametric regression, enhancing convergence rates for spatially inhomogeneous functions.

Findings

Achieves improved convergence rates for spatially inhomogeneous functions.

Retains uniform design properties in standard function classes.

Applicable to a broad range of nonparametric regression problems.

Abstract

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise retains the spatial adaptivity properties of a uniform design.