An efficient kurtosis-based causal discovery method for linear non-Gaussian acyclic data

Understanding the causality behind the observational data is of great importance to a lot of real world applications, e.g., the improvement of Quality of Service. Non-Gaussianity has been exploited in numerous causal discovery methods for observational linear acyclic data. Transforming non-Gaussianity into indirect metrics is a conventional solution employed by existing methods, although this usually results in unreliable estimations or locally optimal solutions. In this work, we employs the excess kurtosis, a direct measure of non-Gaussianity, to establish a causal discovery method for linear non-Gaussian acyclic data. Firstly, we theoretically prove that an exogenous variable has the largest excess kurtosis when disturbance variables follow independent and identically distributions. Secondly, based on this property of exogenous variables, we propose an efficient exogenous variable identification algorithm, and develop a causal discovery method. Extensive experiment results verify the effectiveness and efficiency of the proposed approach.