Rethinking Bivariate Causal Discovery Through the Lens of Exchangeability

Causal discovery methods have traditionally been developed under two different modeling assumptions: independent and identically distributed (i.i.d.) data and time series data. In this paper, we focus on the i.i.d. setting, arguing that it should be reframed in terms of exchangeability, a strictly more general symmetry principle. For that goal, we propose an exchangeable hierarchical model that builds upon the recent Causal de Finetti theorem. Using this model, we show that both the uncertainty regarding the causal mechanism and the uncertainty in the distribution of latent variables are better captured under the broader assumption of exchangeability. In fact, we argue that this is most often the case with real data, as supported by an in-depth analysis of the T\"ubingen dataset. Exploiting this insight, we introduce a novel synthetic dataset that mimics the generation process induced by the proposed exchangeable hierarchical model. We show that our exchangeable synthetic dataset mirrors the statistical and causal structure of the T\"ubingen dataset more closely than other i.i.d. synthetic datasets. Furthermore, we introduce SynthNN, a neural-network-based causal-discovery method trained exclusively on the proposed synthetic dataset. The fact that SynthNN performs competitively with other state-of-the-art methods on the real-world T\"ubingen dataset provides strong evidence for the realism of the underlying exchangeable generative model.