Testing for Association in Multi-View Network Data

TL;DR

This paper develops a hypothesis testing framework to evaluate whether two networks with shared nodes, modeled via stochastic block models, have dependent community structures, with applications to biological interaction data.

Contribution

It introduces a new hypothesis test for independence of community memberships in multi-view network data under stochastic block models.

Findings

Detected weak association between different protein community structures.

Extended the model to incorporate node covariates.

Provided a statistical tool for multi-view network analysis.

Abstract

In this paper, we consider data consisting of multiple networks, each comprised of a different edge set on a common set of nodes. Many models have been proposed for the analysis of such multi-view network data under the assumption that the data views are closely related. In this paper, we provide tools for evaluating this assumption. In particular, we ask: given two networks that each follow a stochastic block model, is there an association between the latent community memberships of the nodes in the two networks? To answer this question, we extend the stochastic block model for a single network view to the two-view setting, and develop a new hypothesis test for the null hypothesis that the latent community memberships in the two data views are independent. We apply our test to protein-protein interaction data from the HINT database (Das and Hint, 2012). We find evidence of a weak association between the latent community memberships of proteins defined with respect to binary interaction data and the latent community memberships of proteins defined with respect to co-complex association data. We also extend this proposal to the setting of a network with node covariates.