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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 ispath-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 frompath 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. 

In general, graph representation learning methods assume that the train and test data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and real-world dataset experiments showcasing the benefits of representations that are invariant to train/test distribution shifts.