Optimal causal inference: estimating stored information and approximating causal architecture.

Area of Science:

• Complex Systems
• Information Theory
• Statistical Inference

Background:

• Inferring causal relationships in complex systems is challenging.
• Stochastic dynamical systems require robust methods for causal architecture determination.
• Existing methods may struggle with finite data and model complexity.

Purpose of the Study:

• To develop a principled approach for inferring the causal architecture of stochastic dynamical systems.
• To extend rate-distortion theory using causal shielding for enhanced causal inference.
• To address both ideal (filtering) and non-ideal (estimation) scenarios with finite data.

Main Methods:

• Utilizing causal shielding, a natural learning principle, to extend rate-distortion theory.
• Developing optimal causal filtering for known probability distributions.
• Implementing optimal causal estimation for finite data scenarios.

Main Results:

• Demonstrated that optimal causal filtering can identify the exact causal architecture (causal-state partition) in ideal conditions.
• Showcased a hierarchy of causal architecture approximations based on model complexity.
• Provided a method to determine the number of causal states from finite data, correcting for statistical fluctuations.

Conclusions:

• The proposed approach offers a principled framework for causal inference in stochastic dynamical systems.
• Causal filtering and estimation provide scalable methods for understanding system structure and information dynamics.
• The methods effectively handle model complexity and finite data limitations, preventing overfitting.