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Bayesian structural inference for hidden processes.

Christopher C Strelioff1, James P Crutchfield2

  • 1Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2014
PubMed
Summary
This summary is machine-generated.

Bayesian structural inference (BSI) discovers complex process patterns using hidden Markov models. This method accurately estimates randomness and structure, reflecting uncertainty for better insights.

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Area of Science:

  • Complex Systems Analysis
  • Computational Neuroscience
  • Information Theory

Background:

  • Inferring the structure of complex processes from data is challenging.
  • Hidden Markov models (HMMs) are powerful tools for time series analysis.
  • ε-machines provide a framework for understanding the dynamics of systems.

Purpose of the Study:

  • To introduce a Bayesian approach for discovering patterns in structurally complex processes.
  • To develop a method for inferring process structure from data series.
  • To quantify process randomness and statistical complexity.

Main Methods:

  • Bayesian structural inference (BSI) using candidate unifilar hidden Markov model (uHMM) topologies.
  • Exact enumeration of topological ε-machines.
  • Analytic expressions for estimating transition probabilities and inferring start states.

Main Results:

  • BSI effectively estimates Shannon entropy rate (randomness) and statistical complexity (structure).
  • The posterior distribution over models better reflects uncertainty than single maximum a posteriori estimation.
  • The method was applied to finite- and infinite-order Markov processes and an infinite-state hidden process.

Conclusions:

  • BSI provides a robust Bayesian framework for structural inference in complex systems.
  • The approach guarantees inferred models are ε-machines.
  • Accurate estimation of process properties and uncertainty is achievable.