Multivariate Granger Causal Discovery for Compressively Sensed Signals

Abstract

Compression-Complexity Causality (CCC) is a recently proposed causality detection method for time series data. It employs complexity estimation techniques based on lossless data-compression algorithms. Along with being formulated as an ‘interventional’ scheme of causality estimation, it overcomes several limitations of traditional causality estimation methods based on Wiener-Granger’s idea, such as the requirement of long-term stationarity and long length data suitable for the estimation of joint probability distributions. It has been shown to be robust for bivariate systems with low temporal resolution, missing samples, long-term memory and finite length data [1]. However, a straightforward extension of CCC for multivariate systems is yet not available. Direct application of bivariate CCC for such systems can give spurious causal estimates, for example, in the presence of indirect and confounding causal variables. In the case when we are interested in determining causal interaction between two observed variables from coupled dynamical systems with multiple variables, the time-delay embedding of the two observables based on Taken’s theorem can help to determine the dynamics of the entire system. Further, the depiction of embedded variables using ordinal patterns-based quantization (symbolization) can help to reduce the dimensionality of the coupled systems to single variable systems. Since the use of ordinal patterns helps to preserve the dynamics of the systems, causal estimation can now be done for these symbolized variables. The technique of ordinal pattern-based coding has been employed in earlier studies for other causality estimation measures such as Transfer Entropy/ Conditional Mutual Information. When used with CCC, this technique combines the strengths of the data-compression and ordinal pattern methodologies, giving promising results on challenging data with irregular and low-resolution sampling, missing samples and short length time series from multivariate systems. We show the performance of this novel ‘permutation CCC’ approach on simulated dynamical systems data and real data from climate system. References: [1] Kathpalia, A., & Nagaraj, N. (2019). Data-based intervention approach for Complexity-Causality measure. PeerJ Computer Science, 5, e196. Authors: Aditi Kathpalia, Pouya Manshour, Milan Paluš Acknowledgements: This study is supported by the Czech Science Foundation, Project No.~GA19-16066S and by the Czech Academy of Sciences, Praemium Academiae awarded to M. Paluš.