CCSL: A Causal Structure Learning Method from Multiple Unknown Environments

Most existing causal structure learning methods require data to be independent and identically distributed (i.i.d.), which often cannot be guaranteed when the data come from different environments. Some previous efforts try to tackle this problem in two independent stages, i.e., first discovering i.i.d. clusters from non-i.i.d. samples, then learning the causal structures from different groups. This straightforward solution ignores the intrinsic connections between the two stages, that is both the clustering stage and the learning stage should be guided by the same causal mechanism. Towards this end, we propose a unified Causal Cluster Structures Learning (named CCSL) method for causal discovery from non-i.i.d. data. This method simultaneously integrates the following two tasks: 1) clustering subjects with the same causal mechanism; 2) learning causal structures from the samples of subjects. Specifically, for the former, we provide a Causality-related Chinese Restaurant Process to cluster samples based on the similarity of the causal structure; for the latter, we introduce a variational-inference-based approach to learn the causal structures. Theoretical results provide identification of the causal model and the clustering model under the linear non-Gaussian assumption. Experimental results on both simulated and real-world data further validate the correctness and effectiveness of the proposed method.