Causal Discovery on Discrete Data via Weighted Normalized Wasserstein Distance

Area of Science:

• Causal inference
• Machine learning
• Statistical modeling

Background:

• Causal discovery from observational data is crucial across scientific disciplines.
• Distinguishing between cause-and-effect relationships (X->Y vs. Y->X) is a fundamental challenge.
• Existing methods may struggle with discrete additive noise models (ANMs).

Purpose of the Study:

• To propose a new method for causal discovery in discrete ANMs.
• To accurately determine the direction of causality from observational data.
• To improve upon state-of-the-art causal discovery techniques.

Main Methods:

• Estimating conditional noise distributions under both causal (X->Y) and anticausal (Y->X) assumptions.
• Leveraging structural properties of discrete ANMs to identify directional differences in noise.
• Employing a weighted normalized Wasserstein distance to quantify noise distribution dissimilarity.

Main Results:

• The dissimilarity of noise distributions is significantly smaller in the true causal direction compared to the anticausal direction.
• The proposed method successfully distinguishes between causal and anticausal relationships.
• Empirical evaluations show strong performance on synthetic data and superiority over existing methods on real-world datasets.

Conclusions:

• The developed method provides a robust approach for causal discovery in discrete ANMs.
• The technique offers improved accuracy and performance compared to current state-of-the-art methods.
• This work contributes a valuable tool for analyzing observational data in various scientific fields.