Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.
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January 2017
Research-Article
Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems
Pileun Kim,
Pileun Kim
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
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Jonathan Rogers,
Jonathan Rogers
Assistant Professor
George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
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Jie Sun,
Jie Sun
Assistant Professor
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Search for other works by this author on:
Erik Bollt
Erik Bollt
Professor
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Search for other works by this author on:
Pileun Kim
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Jonathan Rogers
Assistant Professor
George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Jie Sun
Assistant Professor
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Erik Bollt
Professor
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Department of Mathematics,
Clarkson University,
Potsdam, NY 13699
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 19, 2016; final manuscript received June 29, 2016; published online September 1, 2016. Assoc. Editor: Bogdan I. Epureanu.
J. Comput. Nonlinear Dynam. Jan 2017, 12(1): 011008 (14 pages)
Published Online: September 1, 2016
Article history
Received:
January 19, 2016
Revised:
June 29, 2016
Citation
Kim, P., Rogers, J., Sun, J., and Bollt, E. (September 1, 2016). "Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems." ASME. J. Comput. Nonlinear Dynam. January 2017; 12(1): 011008. https://doi.org/10.1115/1.4034126
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