Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.
['Shohei Shimizu', 'Takanori Inazumi', 'Yasuhiro Sogawa', 'Aapo Hyvärinen', 'Yoshinobu Kawahara', 'Takashi Washio', 'Patrik O. Hoyer', 'Kenneth A. Bollen']
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model