Discovering causal structure with reproducing-kernel Hilbert space ε-machines.

Area of Science:

• Complex Systems Science
• Computational Mechanics
• Machine Learning

Background:

• Inferring causal structure from observational data is crucial for understanding complex systems.
• Existing methods often struggle with high-dimensional, noisy, or continuous data.
• Computational mechanics defines causal states as predictively equivalent histories.

Purpose of the Study:

• To develop a widely applicable method for inferring causal structure directly from system behavior.
• To integrate computational mechanics with reproducing-kernel Hilbert space (RKHS) for representation inference.
• To enable robust prediction for diverse discrete and continuous systems.

Main Methods:

• Merging causal states (computational mechanics) with RKHS representation inference.
• Extracting structural representations (kernel ϵ-machines) via reduced-dimension transforms.
• Estimating evolution operators for stochastic differential equations on causal states.
• Utilizing RKHS functional mapping for prediction in original data space.

Main Results:

• A robust method for inferring causal structure from observed system behaviors.
• Efficient representation of causal states and their topology.
• Accurate prediction capabilities demonstrated on various discrete and continuous processes.
• Successful application to systems with finite/infinite causal states and chaotic flows.

Conclusions:

• The developed method effectively infers causal structure and dynamics from observational data.
• It handles diverse system types, including those with high-dimensional and noisy data.
• This approach advances predictive modeling in complex systems science.