Efficient and Trustworthy Causal Discovery with Latent Variables and Complex Relations

Most traditional causal discovery methods assume that all task-relevant variables are observed, an assumption often violated in practice. Although some recent works allow the presence of latent variables, they typically assume the absence of certain special causal relations to ensure a degree of simplicity, which might also be invalid in real-world scenarios. This paper tackles a challenging and important setting where latent and observed variables are interconnected through complex causal relations. Under a pure children assumption ensuring that latent variables leave adequate footprints in observed variables, we develop novel theoretical results, leading to an efficient causal discovery algorithm which is the first one capable of handling the setting with both latent variables and complex relations within polynomial time. Our algorithm first sequentially identifies latent variables from leaves to roots and then sequentially infers causal relations from roots to leaves. Moreover, we prove trustworthiness of our algorithm, meaning that when the assumption is invalid, it can raise an error signal rather than draw an incorrect causal conclusion, thus preventing potential damage to downstream tasks. We demonstrate the efficacy of our algorithm through experiments. Our work significantly enhances efficiency and reliability of causal discovery in complex systems. Our code is available at: https://github.com/XiuchuanLi/ICLR2025-ETCD