FOM: Fourth-order moment based causal direction identification on the heteroscedastic data.

Identification of the causal direction is a fundamental problem in many scientific research areas. The independence between the noise and the cause variable is a widely used assumption to identify the causal direction. However, such an independence assumption is usually violated due to heteroscedasticity of the real-world data. In this paper, we propose a new criterion for the causal direction identification which is robust to the heteroscedasticity of the data. In detail, the fourth-order moment of noise is proposed to measure the asymmetry between the cause and effect. A heteroscedastic Gaussian process regression-based estimation of the fourth-order moment is proposed accordingly. Under some commonly used assumptions of the causal mechanism, we theoretically show that the noise's fourth-order moment of the causal direction is smaller than that of the anti-causal direction. Experimental results on both simulated and real-world data illustrate the efficiency of the proposed approach.