Mesoscale two-sample testing for networks

TL;DR

This paper introduces a new statistical framework for mesoscale two-sample testing in networks, enabling detection of differences in specific sub-networks or regions across multiple networks, with applications in neuroimaging.

Contribution

It develops projection-based tests for comparing two groups of networks at a mesoscale level, leveraging low-rank projections for increased power, applicable to weighted and binary networks.

Findings

Effective mesoscale testing method for network differences.

Improved power through low-rank projection techniques.

Applicable to neuroimaging and other network-based studies.

Abstract

Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests.