Causal Discovery with Hidden Confounders using the Algorithmic Markov Condition

Causal sufficiency is a cornerstone assumption in causal discovery. It is, however, both unlikely to hold in practice as well as unverifiable. When it does not hold, existing methods struggle to return meaningful results. In this paper, we show how to discover the causal network over both observed and unobserved variables. Moreover, we show that the causal model is identifiable in the sparse linear Gaussian case. More generally, we extend the algorithmic Markov condition to include latent confounders. We propose a consistent score based on the Minimum Description Length principle to discover the full causal network, including latent confounders. Based on this score, we develop an effective algorithm that finds those sets of nodes for which the addition of a confounding factor Z is most beneficial, then fits a new causal network over both observed as well as inferred latent variables.