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

Area of Science:

• Causal Inference
• Statistical Modeling
• Machine Learning

Background:

• Identifying causal direction is crucial in scientific research.
• Standard methods often fail due to heteroscedasticity, violating independence assumptions.
• Real-world data frequently exhibits heteroscedasticity, complicating causal discovery.

Purpose of the Study:

• To develop a robust criterion for causal direction identification.
• To overcome limitations of existing methods in the presence of heteroscedasticity.
• To propose a novel approach leveraging the fourth-order moment of noise.

Main Methods:

• Proposed a new criterion based on the fourth-order moment of noise to measure asymmetry.
• Developed a heteroscedastic Gaussian process regression for estimating the fourth-order moment.
• Theoretically analyzed the criterion under common causal mechanism assumptions.

Main Results:

• Demonstrated that the noise's fourth-order moment differs between causal and anti-causal directions.
• The proposed criterion is theoretically shown to be smaller in the causal direction.
• Experimental validation on simulated and real-world datasets confirmed the approach's efficiency.

Conclusions:

• The proposed fourth-order moment criterion offers a robust solution for causal direction identification.
• The method effectively handles heteroscedasticity, a common issue in observational data.
• This work advances causal discovery techniques for complex, real-world scenarios.