Communication-Efficient Distribution-Free Inference Over Networks

TL;DR

This paper develops communication-efficient, distribution-free inference algorithms for star networks, enabling accurate global error control with minimal communication, applicable to various non-parametric and modern statistical methods.

Contribution

It introduces novel algorithms combining classical and modern inference methods with sampling and quantization for communication-efficient distributed testing.

Findings

Algorithms achieve accurate error control under communication constraints

Methods outperform traditional approaches in simulation studies

Applicable to a wide range of non-parametric and modern inference procedures

Abstract

Consider a star network where each local node possesses a set of test statistics that exhibit a symmetric distribution around zero when their corresponding null hypothesis is true. This paper investigates statistical inference problems in networks concerning the aggregation of this general type of statistics and global error rate control under communication constraints in various scenarios. The study proposes communication-efficient algorithms that are built on established non-parametric methods, such as the Wilcoxon and sign tests, as well as modern inference methods such as the Benjamini-Hochberg (BH) and Barber-Candes (BC) procedures, coupled with sampling and quantization operations. The proposed methods are evaluated through extensive simulation studies.