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Darmon D, Cellucci CJ, Rapp PE. Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures. Chaos. 2019;29(8):083113doi: 10.1063/1.5100742.
Darmon, D., Cellucci, C. J., & Rapp, P. E. (2019). Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures. Chaos (Woodbury, N.Y.), 29(8), 083113. https://doi.org/10.1063/1.5100742
Darmon, David, et al. "Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures." Chaos (Woodbury, N.Y.) vol. 29,8 (2019): 083113. doi: https://doi.org/10.1063/1.5100742
Darmon D, Cellucci CJ, Rapp PE. Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures. Chaos. 2019 Aug;29(8):083113. doi: 10.1063/1.5100742. PMID: 31472514.
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Chaos. 2019 Aug;29(8):083113. doi: 10.1063/1.5100742.

Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures.

Chaos (Woodbury, N.Y.)

David Darmon, Christopher J Cellucci, Paul E Rapp

Affiliations

  1. Department of Mathematics, Monmouth University, West Long Branch, New Jersey 07764, USA.
  2. Aquinas LLC, Berwyn, Pennsylvania 19312, USA.
  3. Traumatic Injury Research Program, Department of Military and Emergency Medicine, Uniformed Services University of the Health Sciences, Bethesda, Maryland 20814, USA.

PMID: 31472514 DOI: 10.1063/1.5100742

Abstract

Information dynamics provides a broad set of measures for characterizing how a dynamical system stores, processes, and transmits information. While estimators for these measures are commonly used in applications, the statistical properties of these estimators for finite time series are not well understood. In particular, the precision of a given estimate is generally unknown. We develop confidence intervals for generic information-dynamic parameters using a bootstrap procedure. The bootstrap procedure uses an echo state network, a particular instance of a reservoir computer, as a simulator to generate bootstrap samples from a given time series. We perform a Monte Carlo analysis to investigate the performance of the bootstrap confidence intervals in terms of their coverage and expected lengths with two model systems and compare their performance to a simulator based on the random analog predictor. We find that our bootstrap procedure generates confidence intervals with nominal, or near nominal, coverage of the information-dynamic measures, with smaller expected length than the random analog predictor-based confidence intervals. Finally, we demonstrate the applicability of the confidence intervals for characterizing the information dynamics of a time series of sunspot counts.

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