Estimating Network Models using Neural Networks

2025-02-03

AI Summary

ERGMs suffer from intractable normalizing constants, rendering conventional MCMC-based maximum likelihood estimation computationally expensive and inherently sequential. To address this, we propose the first end-to-end, deep invertible neural network framework that directly learns a bijective mapping between model parameters and network sufficient statistics—bypassing MCMC sampling entirely. Our method employs supervised learning to jointly train both forward (parameter → statistic) and inverse (statistic → parameter) mappings, accommodating arbitrary differentiable statistics and improving robustness to model misspecification. Evaluated across diverse network datasets, it achieves estimation accuracy comparable to MCMC-MLE while reducing inference latency by one to two orders of magnitude, enabling real-time and batch inference. The core contribution is the first application of invertible neural networks to ERGM estimation, establishing a sampling-free, scalable, and interpretable paradigm. (149 words)

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Estimating network formation models efficiently
• Overcoming intractable normalizing constants in ERGMs
• Using neural networks for fast, parallelizable estimation

Innovation

• Neural network trains parameter-simulation pairs
• Inverts map for fast parallelizable estimation
• Accommodates extra network statistics