Consistent structure estimation of exponential-family random graph models with block structure

Abstract

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs with additional structure in the form of block structure. We have shown elsewhere that when the block structure is known, it facilitates consistency results for $M$-estimators of canonical and curved exponential-family random graph models with complex dependence, such as transitivity. In practice, the block structure is known in some applications (e.g., multilevel networks), but is unknown in others. When the block structure is unknown, the first and foremost question is whether it can be recovered with high probability based on a single observation of a random graph with complex dependence. The main consistency results of the paper show that it is possible to do so under weak dependence and smoothness conditions. These results confirm that exponential-family random graph models with block structure constitute a promising direction of statistical network analysis.

References in corpus (6)

• The method of moments and degree distributions for network models
• Concentration inequalities for dependent Random variables via the martingale method
• Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
• Concentration and consistency results for canonical and curved exponential-family models of random graphs
• A framework for statistical network modeling
• Large-scale estimation of random graph models with local dependence

Cited by in corpus (4)

• Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
• Large-scale estimation of random graph models with local dependence
• Testing biological network motif significance with exponential random graph models
• Improving exponential-family random graph models for bipartite networks