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Full Bayesian identification of linear dynamic systems using stable kernels.

G Pillonetto1, L Ljung2

  • 1Department of Information Engineering, University of Padova, 35131 Padova, Italy.

Proceedings of the National Academy of Sciences of the United States of America
|April 24, 2023
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Summary

This study introduces a new Bayesian approach for system identification using stable kernels, improving model accuracy for complex dynamic systems. The method effectively handles hyperparameters uncertainty, outperforming current state-of-the-art techniques.

Keywords:
Bayesian methodsregularizationsensor and brain networkssystem identification

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Area of Science:

  • Engineering
  • Computer Science
  • Applied Mathematics

Background:

  • System identification models dynamic systems from input-output data.
  • Complex systems in biology and industry require advanced identification techniques.
  • Kernel-based methods offer an alternative to classical system identification.

Purpose of the Study:

  • To develop a full Bayesian framework for linear system identification using stable kernels.
  • To address challenges with hyperparameters uncertainty and model complexity.
  • To overcome limitations of traditional Markov chain Monte Carlo schemes.

Main Methods:

  • Casting stable kernels into a full Bayesian framework.
  • Incorporating hyperparameters uncertainty into dynamic system models.
  • Developing a novel approach to overcome limitations of Markov chain Monte Carlo schemes.

Main Results:

  • The proposed full Bayesian method incorporates hyperparameters uncertainty.
  • Models represent a mixture of dynamic systems across a spectrum of dimensions.
  • Numerical experiments demonstrate superior performance over state-of-the-art methods.
  • Successful application to real-world problems in neural activity and sensor networks.

Conclusions:

  • The full Bayesian approach provides a robust method for linear system identification.
  • This framework effectively models complex dynamic systems with improved accuracy.
  • The method offers a significant advancement for applications in neuroscience and network engineering.