Contextual Stochastic Block Models

TL;DR

This paper provides a rigorous information-theoretic analysis of community detection in sparse graphs with high-dimensional node covariates, establishing the necessity of combining both sources of information for optimal inference.

Contribution

It offers the first tight theoretical analysis for joint inference using graph structure and node covariates, bridging prior heuristic methods and theoretical understanding.

Findings

Proves the information-theoretic necessity of combining graph and covariate data.

Establishes tight bounds for community detection in large-degree networks.

Extends analysis to a Gaussian model variant.

Abstract

We provide the first information theoretic tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same latent communities. Our work bridges recent theoretical breakthroughs in the detection of latent community structure without nodes covariates and a large body of empirical work using diverse heuristics for combining node covariates with graphs for inference. The tightness of our analysis implies in particular, the information theoretical necessity of combining the different sources of information. Our analysis holds for networks of large degrees as well as for a Gaussian version of the model.