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Minimising the Kullback-Leibler Divergence for Model Selection in Distributed Nonlinear Systems.

Oliver M Cliff1,2, Mikhail Prokopenko2, Robert Fitch1,3

  • 1Australian Centre for Field Robotics, The University of Sydney, Sydney NSW 2006, Australia.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

We developed a new method to understand complex systems using Kullback-Leibler (KL) divergence, transfer entropy, and stochastic interaction. This approach helps in selecting models for distributed systems with hidden variables.

Keywords:
Kullback–Leibler divergencecomplex networksinformation theorymodel selectionnonlinear systemsstate space reconstructionstochastic interactiontransfer entropy

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Area of Science:

  • Artificial Intelligence
  • Information Theory
  • Dynamical Systems

Background:

  • Kullback-Leibler (KL) divergence is a key measure in information geometry with broad AI applications.
  • Distributed nonlinear systems with latent variables present challenges for traditional model selection.

Purpose of the Study:

  • To decompose KL divergence for distributed nonlinear systems.
  • To develop a structure learning method for systems with hidden variables.

Main Methods:

  • Decomposition of KL divergence into transfer entropy and stochastic interaction.
  • Utilizing reconstruction theorems and differential topology for analytical solutions.
  • Formulating a transfer entropy-based scoring function for structure learning.

Main Results:

  • An analytical expression for KL divergence in directed acyclic graphs (DAGs) with latent variables was derived.
  • A novel scoring function based on transfer entropy was developed.
  • The method successfully recovered the structure of coupled Lorenz and Rössler systems.

Conclusions:

  • The proposed method offers an exact approach to structure learning in complex distributed systems.
  • Transfer entropy provides a viable scoring mechanism for identifying system dynamics and coupling.
  • This framework advances the analysis of nonlinear dynamical systems in AI.