Assessing significance of information flow in high dimensional dynamical systems with few data

Ross P. Anderson; Maurizio Porfiri

doi:10.1115/DSCC2014-5865

Assessing significance of information flow in high dimensional dynamical systems with few data

Ross P. Anderson, Maurizio Porfiri

Mechanical and Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Information-theoretical notions of causality provide a model-free app roach to identification of the magnitude and direction of influence among sub-components of a stochastic dynamical system. In addition to detecting causal influences, any effective test should also report the level of statistical significance of the finding. Here, we focus on transfer entropy, which has recently been considered for causality detection in a variety of fields based on statistical significance tests that are valid only in the asymptotic regime, that is, with enormous amounts of data. In the interest of app lications with limited available data, we develop a non-asymptotic theory for the probability distribution of the difference between the empirically-estimated transfer entropy and the true transfer entropy. Based on this result, we additionally demonstrate an app roach for statistical hypothesis testing for directed information flow in dynamical systems with a given number of observed time steps.

Original language	English (US)
Title of host publication	Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing
Publisher	American Society of Mechanical Engineers
ISBN (Electronic)	9780791846193
DOIs	https://doi.org/10.1115/DSCC2014-5865
State	Published - 2014
Event	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 - San Antonio, United States Duration: Oct 22 2014 → Oct 24 2014

Publication series

Name	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014
Volume	2

Other

Other	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014
Country/Territory	United States
City	San Antonio
Period	10/22/14 → 10/24/14

ASJC Scopus subject areas

Control and Systems Engineering
Mechanical Engineering
Industrial and Manufacturing Engineering

Access to Document

10.1115/DSCC2014-5865

Cite this

Anderson, R. P., & Porfiri, M. (2014). Assessing significance of information flow in high dimensional dynamical systems with few data. In Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing Article 5865 (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014; Vol. 2). American Society of Mechanical Engineers. https://doi.org/10.1115/DSCC2014-5865

Assessing significance of information flow in high dimensional dynamical systems with few data. / Anderson, Ross P.; Porfiri, Maurizio.
Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing. American Society of Mechanical Engineers, 2014. 5865 (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Anderson, RP & Porfiri, M 2014, Assessing significance of information flow in high dimensional dynamical systems with few data. in Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing., 5865, ASME 2014 Dynamic Systems and Control Conference, DSCC 2014, vol. 2, American Society of Mechanical Engineers, ASME 2014 Dynamic Systems and Control Conference, DSCC 2014, San Antonio, United States, 10/22/14. https://doi.org/10.1115/DSCC2014-5865

Anderson RP, Porfiri M. Assessing significance of information flow in high dimensional dynamical systems with few data. In Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing. American Society of Mechanical Engineers. 2014. 5865. (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014). doi: 10.1115/DSCC2014-5865

Anderson, Ross P. ; Porfiri, Maurizio. / Assessing significance of information flow in high dimensional dynamical systems with few data. Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing. American Society of Mechanical Engineers, 2014. (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014).

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abstract = "Information-theoretical notions of causality provide a model-free app roach to identification of the magnitude and direction of influence among sub-components of a stochastic dynamical system. In addition to detecting causal influences, any effective test should also report the level of statistical significance of the finding. Here, we focus on transfer entropy, which has recently been considered for causality detection in a variety of fields based on statistical significance tests that are valid only in the asymptotic regime, that is, with enormous amounts of data. In the interest of app lications with limited available data, we develop a non-asymptotic theory for the probability distribution of the difference between the empirically-estimated transfer entropy and the true transfer entropy. Based on this result, we additionally demonstrate an app roach for statistical hypothesis testing for directed information flow in dynamical systems with a given number of observed time steps.",

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AB - Information-theoretical notions of causality provide a model-free app roach to identification of the magnitude and direction of influence among sub-components of a stochastic dynamical system. In addition to detecting causal influences, any effective test should also report the level of statistical significance of the finding. Here, we focus on transfer entropy, which has recently been considered for causality detection in a variety of fields based on statistical significance tests that are valid only in the asymptotic regime, that is, with enormous amounts of data. In the interest of app lications with limited available data, we develop a non-asymptotic theory for the probability distribution of the difference between the empirically-estimated transfer entropy and the true transfer entropy. Based on this result, we additionally demonstrate an app roach for statistical hypothesis testing for directed information flow in dynamical systems with a given number of observed time steps.

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Assessing significance of information flow in high dimensional dynamical systems with few data

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