# CopulaGNN: Towards Integrating Representational and Correlational Roles of Graphs in Graph Neural Networks

arXiv: https://arxiv.org/abs/2010.02089 · HTML: https://mlsanity.com/paper/2010.02089/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 10 of 10)

- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [On Generalized Degree Fairness in Graph Neural Networks](https://mlsanity.com/paper/2302.03881/) (2023)
- [Modelling Neighbor Relation in Joint Space-Time Graph for Video Correspondence Learning](https://mlsanity.com/paper/2109.13499/) (2021)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)
- [Multi-label Node Classification On Graph-Structured Data](https://mlsanity.com/paper/2304.10398/) (2023)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Link Prediction without Graph Neural Networks](https://mlsanity.com/paper/2305.13656/) (2023)
- [A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction](https://mlsanity.com/paper/2601.19175/) (2026)
- [Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencoder](https://mlsanity.com/paper/2309.09916/) (2023)

## Abstract (arXiv)

Graph-structured data are ubiquitous. However, graphs encode diverse types of information and thus play different roles in data representation. In this paper, we distinguish the textitrepresentational and the textitcorrelational roles played by the graphs in node-level prediction tasks, and we investigate how Graph Neural Network (GNN) models can effectively leverage both types of information. Conceptually, the representational information provides guidance for the model to construct better node features; while the correlational information indicates the correlation between node outcomes conditional on node features. Through a simulation study, we find that many popular GNN models are incapable of effectively utilizing the correlational information. By leveraging the idea of the copula, a principled way to describe the dependence among multivariate random variables, we offer a general solution. The proposed Copula Graph Neural Network (CopulaGNN) can take a wide range of GNN models as base models and utilize both representational and correlational information stored in the graphs. Experimental results on two types of regression tasks verify the effectiveness of the proposed method.