Causal Discovery with Multi-Domain LiNGAM for Latent Factors
Proceedings of The 2021 Causal Analysis Workshop Series, PMLR 160:1-4, 2021.
Discovering causal structures among latent factors from observed data is particularly significant yet challenging problem. Despite some efforts for this problem, existing methods focus on the single-domain data only. In this paper, we propose Multi-Domain Linear Non-Gaussian Acyclic Models for LAtent Factors (MD-LiNA), where the causal structures from different domains may be different, but they have a shared causal structure among latent factors of interest. The model enriches the causal representation for multi-domain data. We propose an integrated two-phase algorithm to estimate the model. In particular, we first locate the latent factors and estimate the factor loading matrix. Then to uncover the shared causal structure among latent factors of interest, we derive a score function based on the characterization of independence relations between external influences and the dependence relations between multi-domain latent factors and latent factors of interest. Experimental results on synthetic data demonstrate the efficacy of our approach.