Nonlinear Causal Discovery with Latent Confounders

Causal discovery, the task of discovering the causal graph over a set of observed variables $X_1,\ldots,X_m$, is a challenging problem. One of the cornerstone assumptions is that of causal sufficiency: that all common causes of all measured variables have been observed. When it does not hold, causal discovery algorithms making this assumption return networks with many spurious edges. In this paper, we propose a nonlinear causal model involving hidden confounders. We show that it is identifiable from only the observed data and propose an efficient method for recovering this causal model. At the heart of our approach is a variational autoencoder which parametrizes both the causal interactions between observed variables as well as the influence of the unobserved confounders. Empirically we show that it outperforms other state-of-the-art methods for causal discovery under latent confounding on synthetic and real-world data.