# A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network

arXiv: https://arxiv.org/abs/1806.11220 · HTML: https://mlsanity.com/paper/1806.11220/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [EDoG: Adversarial Edge Detection For Graph Neural Networks](https://mlsanity.com/paper/2212.13607/) (2022)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Block Dense Weighted Networks with Augmented Degree Correction](https://mlsanity.com/paper/2105.12290/) (2021)
- [Spectral goodness-of-fit tests for complete and partial network data](https://mlsanity.com/paper/2106.09702/) (2021)
- [Goodness-of-Fit of Attributed Probabilistic Graph Generative Models](https://mlsanity.com/paper/2308.03773/) (2023)

## Abstract (arXiv)

Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies amongst these actors, these dependencies imply the lack of independence. This poses statistical challenges for analyzing such data, especially when there is only a single observed network, and often leads to intractable likelihoods regardless of the modeling paradigm, which limit the application of existing statistical methods for networks. We explore a subsampling bootstrap procedure to serve as the basis for goodness of fit and model selection with a single observed network that circumvents the intractability of such likelihoods. Our approach is based on flexible resampling distributions formed from the single observed network, allowing for finer and higher dimensional comparisons than simply point estimates of quantities of interest. We include worked examples for model selection, with simulation, and assessment of goodness of fit, with duplication-divergence model fits for yeast (S.cerevisiae) protein-protein interaction data from the literature. The proposed procedure produces a flexible resampling distribution that can be based on any statistics of one's choosing and can be employed regardless of choice of model.