Information Theoretic Derivations for Causality Detection: Application to Human Gait

As a causality criterion we propose the conditional relative entropy. The relationship with information theoretic functionals mutual information and entropy is established. The conditional relative entropy criterion is compared with 3 well-established techniques for causality detection: 'Sims', 'Geweke-Meese-Dent' and 'Granger'. It is shown that the conditional relative entropy, as opposed to these 3 criteria, is sensitive to0. non-linear causal relationships. All results are illustrated on real-world time series of human gait.

[1]  M Palus,et al.  Synchronization as adjustment of information rates: detection from bivariate time series. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[3]  Katsunori Ikoma,et al.  Obituary: Yukio Mano (1943–2004) , 2005, Journal of NeuroEngineering and Rehabilitation.

[4]  C. Hafner,et al.  Testing causality in variance using multivariate GARCH models , 2004 .

[5]  Jeffrey M. Hausdorff,et al.  Falls and freezing of gait in Parkinson's disease: A review of two interconnected, episodic phenomena , 2004, Movement disorders : official journal of the Movement Disorder Society.

[6]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[7]  Jeffrey M. Hausdorff,et al.  When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations. , 2001, Physica A.

[8]  John Geweke,et al.  Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence☆ , 1983 .

[9]  Liam Paninski,et al.  Estimation of Entropy and Mutual Information , 2003, Neural Computation.

[10]  Heidelberg,et al.  Encircling an exceptional point. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  J Hausdroff.  Gait variability : methods, modeling and meaning , 2005 .

[12]  Stefano Longhi.  Spiral waves in optical parametric oscillators , 2001 .

[13]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[14]  Michael McAleer,et al.  ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL , 2003, Econometric Theory.

[15]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.