  Discovering causal structures among latent factors from observed data is a
particularly 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 structure among latent factors of interest is
shared for all domains, and we provide its identification results. 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 causal structure among shared 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. We show that the proposed method
provides locally consistent estimators. Experimental results on both synthetic
and real-world data demonstrate the efficacy and robustness of our approach.
