Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Model

We present new measures of the causal direction between two non-gaussian random variables. They are based on the likelihood ratio under the linear non-gaussian acyclic model (LiNGAM). We also develop simple first-order approximations and analyze them based on related cumulant-based measures. The cumulant-based measures can be shown to give the right causal directions, and they are statistically consistent even in the presence of measurement noise. We further show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple.