Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data

TL;DR

This paper introduces a fast equilibrium expectation algorithm for maximum likelihood estimation in large network data, significantly expanding the size of networks analyzable with ERGMs by leveraging Markov chain properties.

Contribution

The paper presents a novel equilibrium expectation algorithm that enables efficient MLE for large-scale networks within exponential random graph models.

Findings

The EE algorithm significantly increases the maximum network size for ERGM analysis.

Application to biological and social networks demonstrates scalability and effectiveness.

Empirical results show accurate parameter estimation in networks with over 100,000 nodes.

Abstract

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach becomes increasingly problematic as network size increases. In the context of current research on efficient estimation of models for large network data sets, we propose a fast algorithm for maximum likelihood estimation (MLE) that afords a signifcant increase in the size of networks amenable to direct empirical analysis. The algorithm we propose in this paper relies on properties of Markov chains at equilibrium, and for this reason it is called equilibrium expectation (EE). We demonstrate the performance of the EE algorithm in the context of exponential random graphmodels (ERGMs) a family of statistical models commonly used in empirical research based on network data observed at a single period in time. Thus far, the lack of efcient computational strategies has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The approach we propose allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes