Information-theoretical notions of causality provide a model-free approach 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 applications 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 approach for statistical hypothesis testing for directed information flow in dynamical systems with a given number of observed time steps.
- Dynamic Systems and Control Division
Assessing Significance of Information Flow in High Dimensional Dynamical Systems With Few Data
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Anderson, RP, & Porfiri, M. "Assessing Significance of Information Flow in High Dimensional Dynamical Systems With Few Data." Proceedings of the ASME 2014 Dynamic Systems and Control Conference. Volume 2: 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. San Antonio, Texas, USA. October 22–24, 2014. V002T24A002. ASME. https://doi.org/10.1115/DSCC2014-5865
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