Latent Community Adaptive Network Regression

TL;DR

This paper introduces a latent community adaptive network regression model that jointly detects communities and estimates covariate effects, accounting for community-specific variations to improve accuracy in network analysis.

Contribution

It presents a novel latent space network model with community-dependent covariate effects and an MCMC method for joint community detection and coefficient estimation.

Findings

Jointly modeling communities and covariate effects improves edge prediction.

Spectral methods enhance computational efficiency.

Ignoring community structure can bias covariate importance estimates.

Abstract

The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it is likely that the effects of covariates on edge formation differ between communities (e.g. age might play a different role in friendship formation in communities across a city). In this work, we introduce a latent space network model where coefficients associated with certain covariates can depend on latent community membership of the nodes. We show that ignoring such structure can lead to either over- or under-estimation of covariate importance to edge formation and propose a Markov Chain Monte Carlo approach for simultaneously learning the latent community structure and the community specific coefficients. We leverage efficient spectral methods to improve the computational tractability of our approach.