Local Causal Discovery Without Causal Sufficiency

Local causal discovery is crucial for revealing the causal relationships between specific variables from data. Existing local causal discovery algorithms are designed under the assumption of causal sufficiency, which states that there are no latent common causes for two or more of the observed variables in data. However, the assumption of causal sufficiency is often violated in practice. To address this issue, we first propose the local Maximal Ancestral Graph (MAG), referred to as LocalMAG, to describe the local causal relationships of the target variable in the MAG. Then, we propose a local causal discovery algorithm without the assumption of causal sufficiency, called LatentLCD, to learn the LocalMAG. Specifically, LatentLCD first uses the traditional parents and children discovery algorithm to identify the local causal skeleton that includes latent variables and verifies it theoretically. It then identifies bidirectional edges by determining whether both the target variable and its adjacent variables are colliders, thereby identifying latent variables in the local structure of the target variable. Extensive experiments on synthetic datasets have validated that the proposed LatentLCD algorithm significantly outperforms the state-of-the-art methods.