# Neural Posterior Estimation on Exponential Random Graph Models: Evaluating Bias and Implementation Challenges

arXiv: https://arxiv.org/abs/2504.09349 · HTML: https://mlsanity.com/paper/2504.09349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 12 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [ABC of the Future](https://mlsanity.com/paper/2112.12841/) (2021)
- [Highly Scalable Maximum Likelihood and Conjugate Bayesian Inference for ERGMs on Graph Sets with Equivalent Vertices](https://mlsanity.com/paper/2110.13527/) (2021)
- [Copula Approximate Bayesian Computation Using Distribution Random Forests](https://mlsanity.com/paper/2402.18450/) (2024)
- [Estimating Network Models using Neural Networks](https://mlsanity.com/paper/2502.01810/) (2025)

## Abstract (arXiv)

Exponential random graph models (ERGMs) are flexible probabilistic frameworks to model statistical networks through a variety of network summary statistics. Conventional Bayesian estimation for ERGMs involves iteratively exchanging with an auxiliary variable due to the intractability of ERGMs, however, this approach lacks scalability to large-scale implementations. Neural posterior estimation (NPE) is a recent advancement in simulation-based inference, using a neural network based density estimator to infer the posterior for models with doubly intractable likelihoods for which simulations can be generated. While NPE has been successfully adopted in various fields such as cosmology, little research has investigated its use for ERGMs. Performing NPE on ERGM not only provides a differing angle of resolving estimation for the intractable ERGM likelihoods but also allows more efficient and scalable inference using the amortisation properties of NPE, and therefore, we investigate how NPE can be effectively implemented in ERGMs. In this study, we present the first systematic implementation of NPE for ERGMs, rigorously evaluating potential biases, interpreting the biases magnitudes, and comparing NPE fittings against conventional Bayesian ERGM fittings. More importantly, our work highlights ERGM-specific areas that may impose particular challenges for the adoption of NPE.