# Causal Lifting and Link Prediction

arXiv: https://arxiv.org/abs/2302.01198 · HTML: https://mlsanity.com/paper/2302.01198/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 101 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 30 of 38)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning](https://mlsanity.com/paper/2010.16103/) (2020)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Causal Embeddings for Recommendation](https://mlsanity.com/paper/1706.07639/) (2017)
- [On the Benefits of Invariance in Neural Networks](https://mlsanity.com/paper/2005.00178/) (2020)
- [Neo-GNNs: Neighborhood Overlap-aware Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2206.04216/) (2022)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [Sequence-Aware Recommender Systems](https://mlsanity.com/paper/1802.08452/) (2018)
- [Learning Individual Causal Effects from Networked Observational Data](https://mlsanity.com/paper/1906.03485/) (2019)
- [Graph cluster randomization: network exposure to multiple universes](https://mlsanity.com/paper/1305.6979/) (2013)
- [Design and analysis of experiments in networks: Reducing bias from interference](https://mlsanity.com/paper/1404.7530/) (2014)
- [Ontology Reasoning with Deep Neural Networks](https://mlsanity.com/paper/1808.07980/) (2018)
- [OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs](https://mlsanity.com/paper/2205.15117/) (2022)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [Neural Network Matrix Factorization](https://mlsanity.com/paper/1511.06443/) (2015)
- [Addressing Marketing Bias in Product Recommendations](https://mlsanity.com/paper/1912.01799/) (2019)

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

- [A Multi-Task Perspective for Link Prediction with New Relation Types and Nodes](https://mlsanity.com/paper/2307.06046/) (2023)
- [End-To-End Causal Effect Estimation from Unstructured Natural Language Data](https://mlsanity.com/paper/2407.07018/) (2024)
- [Expressive Sign Equivariant Networks for Spectral Geometric Learning](https://mlsanity.com/paper/2312.02339/) (2023)
- [Heterophilic Graph Neural Networks Optimization with Causal Message-passing](https://mlsanity.com/paper/2411.13821/) (2024)
- [Are Heterogeneous Graph Neural Networks Truly Effective for Node Classification? A Causal Perspective](https://mlsanity.com/paper/2510.05750/) (2025)

## Abstract (arXiv)

Existing causal models for link prediction assume an underlying set of inherent node factors -- an innate characteristic defined at the node's birth -- that governs the causal evolution of links in the graph. In some causal tasks, however, link formation is path-dependent: The outcome of link interventions depends on existing links. Unfortunately, these existing causal methods are not designed for path-dependent link formation, as the cascading functional dependencies between links (arising from path dependence) are either unidentifiable or require an impractical number of control variables. To overcome this, we develop the first causal model capable of dealing with path dependencies in link prediction. In this work we introduce the concept of causal lifting, an invariance in causal models of independent interest that, on graphs, allows the identification of causal link prediction queries using limited interventional data. Further, we show how structural pairwise embeddings exhibit lower bias and correctly represent the task's causal structure, as opposed to existing node embeddings, e.g., graph neural network node embeddings and matrix factorization. Finally, we validate our theoretical findings on three scenarios for causal link prediction tasks: knowledge base completion, covariance matrix estimation and consumer-product recommendations.