Discovery of Linear Non-Gaussian Acyclic Models in the Presence of Latent Classes

An effective way to examine causality is to conduct an experiment with random assignment. However, in many cases it is impossible or too expensive to perform controlled experiments, and hence one often has to resort to methods for discovering good initial causal models from data which do not come from such controlled experiments. We have recently proposed such a discovery method based on independent component analysis (ICA) called LiNGAM and shown how to completely identify the data generating process under the assumptions of linearity, non-gaussianity, and no latent variables. In this paper, after briefly recapitulating this approach, we extend the framework to cases where latent classes (hidden groups) are present. The model identification can be accomplished using a method based on ICA mixtures. Simulations confirm the validity of the proposed method.