Determining Causal Skeletons with Information Theory

Area of Science:

• Causal inference and network analysis.
• Information theory and stochastic processes.
• Linear algebra and tensor decomposition.

Background:

• Causal discovery often relies on complex conditional independence tests.
• Existing methods can be computationally intensive and require high-dimensional data.
• Modeling causal links as communication channels offers a new perspective.

Discussion:

• Stochastic tensors fully characterize communication channels between variables.
• Linear algebra operations on these tensors simplify causal inference.
• This tensor-based method reduces the data dimensionality required for analysis.

Key Insights:

• Pair-wise determined tensors are sufficient for inferring causal skeletons in three-variable systems.
• The concept of path information from information theory is crucial.
• This approach streamlines the discovery of causal structures.

Outlook:

• Potential for application in complex systems with numerous variables.
• Integration with advanced machine learning techniques for causal discovery.
• Further exploration of information-theoretic extensions for causal modeling.