An asymptotic analysis of distributed nonparametric methods

TL;DR

This paper analyzes the fundamental performance of distributed nonparametric learning methods using a Gaussian noise model, emphasizing the impact of design choices on convergence and uncertainty quantification.

Contribution

It provides an asymptotic comparison of distributed nonparametric methods within a benchmark Gaussian noise model, highlighting challenges in automatic adaptation to smoothness.

Findings

Design and tuning significantly affect convergence rates.

Uncertainty quantification validity depends on method design.

Automatic adaptation to smoothness remains challenging.

Abstract

We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which serves as a benchmark model for studying performance in this setting. The results show how the design and tuning of a distributed method can have great impact on convergence rates and validity of uncertainty quantification. Moreover, we highlight the difficulty of designing nonparametric distributed procedures that automatically adapt to smoothness.