Source-linked AI summary
A Bayesian Approach to Network Modularity
Jake M. Hofman, Chris H. Wiggins
TL;DR
Community detection requires choosing what to optimize and how many modules to infer. The paper formulates module detection as Bayesian inference with variational Bayes, recovering module assignments and model complexity while addressing the resolution limit.
Problem
Existing community-detection methods often optimize fixed-parameter cost functions, while the choice of what to optimize and the number of modules receive less attention.
Method
The approach uses a constrained stochastic block model with Bayesian evidence, parameter priors, and variational Bayes to infer module assignments, parameters, and the number of modules.
Results
The method identifies the evidence-maximizing number of occupied modules, avoids resolution-limit problems, and recovers 12 NCAA football conferences with 105 of 115 teams assigned to their corresponding conferences.
Takeaways & Limitations
Inferring distributions over model parameters reveals a network's natural modular scale and permits principled selection among nested and different parametric models.
Takeaways & Limitations
Expectation-maximization is prone to overfitting and cannot determine the appropriate number of modules because observed-data likelihood increases with model size.
Abstract
from arXiv · showhide
We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcomes the resolution limit problem, accurately recovering the true number of modules. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We apply the technique to synthetic and real networks and outline how the method naturally allows selection among competing models.