Causal discovery via reproducing kernel Hilbert space embeddings.

Area of Science:

• Causal inference and machine learning.
• Statistical modeling and data analysis.

Background:

• Inferring causal direction from observational data is challenging.
• Existing methods often rely on independence assumptions that may not hold universally.
• Exploiting asymmetries between cause and effect distributions offers a promising avenue for causal discovery.

Discussion:

• The study defines an uncorrelatedness criterion between cause and conditional effect distributions.
• It proposes a complexity metric to quantify asymmetry, showing it's less in the causal direction.
• A Hilbert space embedding method (EMD) is introduced to compute this metric effectively.

Key Insights:

• A novel kernel-based algorithm for causal discovery is presented, leveraging the proposed complexity metric.
• The method accommodates general cause-to-effect transformations, including noise effects.
• Applicable to both one-dimensional and high-dimensional data, and capable of inferring multi-variable causal orderings.

Outlook:

• The proposed method demonstrates effectiveness through extensive experiments on simulated and real-world data.
• Potential for broader applications in fields requiring robust causal inference.
• Further research could explore extensions to dynamic systems or non-linear causal mechanisms.