Estimating Network Models using Neural Networks

TL;DR

The paper tackles the estimation bottleneck in Exponential Random Graph Models (ERGMs), where the intractable normalizing constant $c(\theta)$ complicates likelihood-based inference. It introduces a neural-network surrogate that learns the map $\theta \mapsto E[t(g,\theta)]$ offline from a large, parallelizable design of parameter–simulation pairs, and then solves $\min_{\theta} \| f_\phi(\theta) - t_{obs} \|$ to recover the observed parameters, effectively decoupling simulation from inference. This approach enables scalable, parallel training, accommodates extra statistics to mitigate misspecification, and offers a built-in goodness-of-fit check during training. While promising for large and curved ERGMs, the method relies on identifiability of the map and incurs substantial upfront simulations, with future work aimed at real-data applications, heterogeneity, and standard-error computation.

Abstract

Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential simulation at every optimization step. We propose a neural network approach that trains on a single, large set of parameter-simulation pairs to learn the mapping from parameters to average network statistics. Once trained, this map can be inverted, yielding a fast and parallelizable estimation method. The procedure also accommodates extra network statistics to mitigate model misspecification. Some simple illustrative examples show that the method performs well in practice.

Figures (3)

• Figure 1: Predicted vs test data, model with edges only
• Figure 2: Training data vs. predicted vs Theoretical number of links, models with edges only
• Figure 3: Predicted vs test data, model with edges and mutual links