# Learning from Counterfactual Links for Link Prediction

arXiv: https://arxiv.org/abs/2106.02172 · HTML: https://mlsanity.com/paper/2106.02172/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 99 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 30 of 43)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)

## Built on by (most cited first, 30 of 69)

- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Graph Neural Networks for Link Prediction with Subgraph Sketching](https://mlsanity.com/paper/2209.15486/) (2022)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalization](https://mlsanity.com/paper/2210.02016/) (2022)
- [MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initialization](https://mlsanity.com/paper/2210.00102/) (2022)
- [GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentation](https://mlsanity.com/paper/2310.00800/) (2023)
- [Global Counterfactual Explainer for Graph Neural Networks](https://mlsanity.com/paper/2210.11695/) (2022)
- [PaGE-Link: Path-based Graph Neural Network Explanation for Heterogeneous Link Prediction](https://mlsanity.com/paper/2302.12465/) (2023)
- [Towards Fair Graph Neural Networks via Graph Counterfactual](https://mlsanity.com/paper/2307.04937/) (2023)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Data-Centric Learning from Unlabeled Graphs with Diffusion Model](https://mlsanity.com/paper/2303.10108/) (2023)
- [Modeling Dynamic Environments with Scene Graph Memory](https://mlsanity.com/paper/2305.17537/) (2023)
- [On Strengthening and Defending Graph Reconstruction Attack with Markov Chain Approximation](https://mlsanity.com/paper/2306.09104/) (2023)
- [Semi-Supervised Graph Imbalanced Regression](https://mlsanity.com/paper/2305.12087/) (2023)
- [Knowledge Graph Completion with Counterfactual Augmentation](https://mlsanity.com/paper/2302.13083/) (2023)
- [Collaboration-Aware Graph Convolutional Network for Recommender Systems](https://mlsanity.com/paper/2207.06221/) (2022)
- [FakeEdge: Alleviate Dataset Shift in Link Prediction](https://mlsanity.com/paper/2211.15899/) (2022)
- [Link Prediction with Non-Contrastive Learning](https://mlsanity.com/paper/2211.14394/) (2022)
- [A Topological Perspective on Demystifying GNN-Based Link Prediction Performance](https://mlsanity.com/paper/2310.04612/) (2023)
- [Optimizing Long-tailed Link Prediction in Graph Neural Networks through Structure Representation Enhancement](https://mlsanity.com/paper/2407.20499/) (2024)
- [Exploring Causal Learning through Graph Neural Networks: An In-depth Review](https://mlsanity.com/paper/2311.14994/) (2023)
- [Cross-Domain Graph Data Scaling: A Showcase with Diffusion Models](https://mlsanity.com/paper/2406.01899/) (2024)
- [GiGL: Large-Scale Graph Neural Networks at Snapchat](https://mlsanity.com/paper/2502.15054/) (2025)
- [Addressing Shortcomings in Fair Graph Learning Datasets: Towards a New Benchmark](https://mlsanity.com/paper/2403.06017/) (2024)

## Abstract (arXiv)

Learning to predict missing links is important for many graph-based applications. Existing methods were designed to learn the association between observed graph structure and existence of link between a pair of nodes. However, the causal relationship between the two variables was largely ignored for learning to predict links on a graph. In this work, we visit this factor by asking a counterfactual question: "would the link still exist if the graph structure became different from observation?" Its answer, counterfactual links, will be able to augment the graph data for representation learning. To create these links, we employ causal models that consider the information (i.e., learned representations) of node pairs as context, global graph structural properties as treatment, and link existence as outcome. We propose a novel data augmentation-based link prediction method that creates counterfactual links and learns representations from both the observed and counterfactual links. Experiments on benchmark data show that our graph learning method achieves state-of-the-art performance on the task of link prediction.