# Goodness-of-Fit of Attributed Probabilistic Graph Generative Models

arXiv: https://arxiv.org/abs/2308.03773 · HTML: https://mlsanity.com/paper/2308.03773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 28 Jul 2023.

## Builds on (most cited first, 9 of 9)

- [Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation](https://mlsanity.com/paper/2010.16061/) (2020)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Clustering attributed graphs: models, measures and methods](https://mlsanity.com/paper/1501.01676/) (2015)
- [Edge-exchangeable graphs and sparsity](https://mlsanity.com/paper/1603.06898/) (2016)
- [A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network](https://mlsanity.com/paper/1806.11220/) (2018)
- [Spectral goodness of fit for network models](https://mlsanity.com/paper/1407.7247/) (2014)
- [Block-Approximated Exponential Random Graphs](https://mlsanity.com/paper/2002.07076/) (2020)
- [On RKHS Choices for Assessing Graph Generators via Kernel Stein Statistics](https://mlsanity.com/paper/2210.05746/) (2022)
- [Edge exchangeable models for network data](https://mlsanity.com/paper/1603.04571/) (2016)

## Abstract (arXiv)

Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also their attributes. However, given a generative model of random attributed graph(s), the general conditions that establish goodness of fit are not clear a-priori. In this paper, we define goodness of fit in terms of the mean square contingency coefficient for random binary networks. For this statistic, we outline a procedure for assessing the quality of the structure of a learned attributed graph by ensuring that the discrepancy of the mean square contingency coefficient (constant, or random) is minimal with high probability. We apply these criteria to verify the representation capability of a probabilistic generative model for various popular types of graph models.