# Selection of Exponential-Family Random Graph Models via Held-Out Predictive Evaluation (HOPE)

arXiv: https://arxiv.org/abs/1908.05873 · HTML: https://mlsanity.com/paper/1908.05873/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)

## Abstract (arXiv)

Statistical models for networks with complex dependencies pose particular challenges for model selection and evaluation. In particular, many well-established statistical tools for selecting between models assume conditional independence of observations and/or conventional asymptotics, and their theoretical foundations are not always applicable in a network modeling context. While simulation-based approaches to model adequacy assessment are now widely used, there remains a need for procedures that quantify a model's performance in a manner suitable for selecting among competing models. Here, we propose to address this issue by developing a predictive evaluation strategy for exponential family random graph models that is analogous to cross-validation. Our approach builds on the held-out predictive evaluation (HOPE) scheme introduced by Wang et al. (2016) to assess imputation performance. We systematically hold out parts of the observed network to: evaluate how well the model is able to predict the held-out data; identify where the model performs poorly based on which data are held-out, indicating e.g. potential weaknesses; and calculate general summaries of predictive performance that can be used for model selection. As such, HOPE can assist researchers in improving models by indicating where a model performs poorly, and by quantitatively comparing predictive performance across competing models. The proposed method is applied to model selection problem of two well-known data sets, and the results are compared to those obtained via nominal AIC and BIC scores.