Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models
Aapo Hyvarinen (University of Helsinki);
JMLR W&P 13:1-16, 2010.
We present new measures of the causal direction between two nongaussian
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.