# Computing Expected Motif Counts for Exchangeable Graph Generative Models

arXiv: https://arxiv.org/abs/2305.01089 · HTML: https://mlsanity.com/paper/2305.01089/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 9 references that are in the map.
- First posted on arXiv 1 May 2023.

## Builds on (most cited first, 6 of 6)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [Learning Bayesian Networks Under Sparsity Constraints: A Parameterized Complexity Analysis](https://mlsanity.com/paper/2004.14724/) (2020)
- [Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders](https://mlsanity.com/paper/2210.16844/) (2022)

## Abstract (arXiv)

Estimating the expected value of a graph statistic is an important inference task for using and learning graph models. This note presents a scalable estimation procedure for expected motif counts, a widely used type of graph statistic. The procedure applies for generative mixture models of the type used in neural and Bayesian approaches to graph data.