Parameter identifiability in a class of random graph mixture models

TL;DR

This paper proves that parameters in a broad class of random graph mixture models, including stochastic blockmodels and their weighted variants, are identifiable, which is crucial for reliable parameter estimation.

Contribution

It provides a comprehensive proof of parameter identifiability for a wide class of random graph mixture models, extending previous limited results.

Findings

Parameters are identifiable in binary and weighted random graph models.

Revisits and clarifies the estimation procedure for binary affiliation models.

Implications for consistent parameter estimation in network models.

Abstract

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are independent random variables when conditioned on the groups of the nodes being connected. In the binary random graph case, in which edges are either present or absent, these models are known as stochastic blockmodels and have been widely used in the social sciences and, more recently, in biology. Their generalizations to weighted random graphs, either in parametric or non-parametric form, are also of interest in many areas. Despite a broad range of applications, the parameter identifiability issue for such models is involved, and previously has only been touched upon in the literature. We give here a thorough investigation of this problem. Our work also has consequences for parameter estimation. In particular, the estimation procedure proposed by Frank and Harary for binary affiliation models is revisited in this article.