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

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This study introduces a new method to infer system causal structure from observed behaviors using computational mechanics and reproducing-kernel Hilbert space (RKHS). The technique robustly identifies underlying dynamics across diverse systems, enhancing predictive modeling capabilities.

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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.