Efficient inference in stochastic block models with vertex labels
This work addresses community detection in networks with side information, offering incremental improvements for researchers in statistical inference and network analysis.
The authors tackled the problem of community detection in stochastic block models with vertex labels by analyzing a linearized belief propagation algorithm, showing it achieves optimal accuracy when a specific function of network parameters has a unique fixed point, and that increasing label information can reduce fixed points to enable optimal performance.
We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a linearized version of the popular belief propagation algorithm. We show that this algorithm achieves the highest accuracy possible whenever a certain function of the network parameters has a unique fixed point. Whenever this function has multiple fixed points, the belief propagation algorithm may not perform optimally. We show that increasing the information in the vertex labels may reduce the number of fixed points and hence lead to optimality of belief propagation.