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A Synergistic Perspective on Multivariate Computation and Causality in Complex Systems.

Thomas F Varley1

  • 1Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA.

Entropy (Basel, Switzerland)
|October 25, 2024
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Summary

Complex systems perform computations when their state depends on multiple inputs. This study links statistical synergy, a measure of joint input information, to causal inference, offering a new theory of computation.

Keywords:
Berkson’s paradoxhigher-order interactionsmultivariate information theorypartial information decompositionsynergy

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Area of Science:

  • Complex Systems Science
  • Information Theory
  • Causal Inference

Background:

  • Defining computation in complex systems is challenging.
  • Existing approaches may not fully capture multivariate input dependencies.
  • Statistical synergy offers a novel perspective on information processing.

Purpose of the Study:

  • To establish a general framework for studying computation in complex systems.
  • To connect statistical synergy with causal inference, particularly causal colliders.
  • To develop a mathematically rich theory of computation.

Main Methods:

  • Utilizing multivariate information theory to define and quantify statistical synergy.
  • Applying concepts from causal inference, including causal colliders and Berkson's paradox.
  • Investigating the relationship between empirical synergies and genuine computation.

Main Results:

  • Statistical synergy quantifies information uniquely available from joint inputs.
  • A direct link is established between statistical synergy and causal colliders.
  • Berkson's paradox illustrates synergistic interactions in multidimensional systems.
  • Causal structure learning helps distinguish genuine computation from spurious synergies.

Conclusions:

  • Statistical synergy provides a powerful tool for understanding computation in complex systems.
  • The framework bridges information theory and causal inference for a unified theory.
  • This approach lays the groundwork for a general mathematical theory of computation.