Highly scalable maximum likelihood and conjugate Bayesian inference for ERGMs on graph sets with equivalent vertices.

Area of Science:

• Network analysis
• Statistical modeling
• Computational statistics

Background:

• Exponential family random graph models (ERGMs) are flexible for network analysis.
• Current ERGM inference methods, like MCMC MLE, are computationally expensive, especially for large networks or pooled data.
• Existing Bayesian methods for ERGMs are even more computationally demanding on large graphs.

Purpose of the Study:

• To develop a computationally efficient approach for ERGM inference in the pooled case.
• To enable analysis of multiple networks without prohibitive increases in computational cost.
• To facilitate Bayesian inference for ERGMs, including pooled data, with computational efficiency.

Main Methods:

• Exploiting properties of discrete exponential families for pooled ERGM inference.
• Developing a variant for Bayesian inference using conjugate priors.
• Applying the methods to pooled analysis of brain functional connectivity and crystal structure networks.

Main Results:

• The proposed pooled method fits an arbitrary number of graph observations with minimal computational overhead beyond data preprocessing.
• Bayesian inference under conjugate priors is computationally inexpensive during the estimation phase.
• Simulation studies confirm good frequentist properties for pooled estimates and well-behaved posterior estimates.

Conclusions:

• The new approach offers a computationally efficient solution for pooled ERGM inference.
• It extends efficient Bayesian inference capabilities for ERGMs, suitable for regularization.
• The method is demonstrated to be effective on real-world network data, including brain connectivity and protein structures.