title: Detecting causality from nonlinear dynamics with short-term time series.
abstract: Quantifying causality between variables from observed time series data is of great importance in various disciplines but also a challenging task, especially when the observed data are short. Unlike the conventional methods, we find it possible to detect causality only with very short time series data, based on embedding theory of an attractor for nonlinear dynamics. Specifically, we first show that measuring the smoothness of a cross map between two observed variables can be used to detect a causal relation. Then, we provide a very effective algorithm to computationally evaluate the smoothness of the cross map, or "Cross Map Smoothness" (CMS), and thus to infer the causality, which can achieve high accuracy even with very short time series data. Analysis of both mathematical models from various benchmarks and real data from biological systems validates our method.
authors.affiliation: 1] School of Mathematical Sciences, Soochow University, China [2] Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Japan.
authors.forename: Huanfei
authors.initials: H
authors.lastname: Ma
authors.affiliation: Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Japan.
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
authors.affiliation: 1] Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Japan [2] Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, China.
authors.forename: Luonan
authors.initials: L
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D015984:Causality; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D029968:Escherichia coli Proteins / Q000235:genetics*; D053263:Gene Regulatory Networks; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D029701:Saccharomyces cerevisiae Proteins / Q000235:genetics*; D013997:Time Factors
chemical_list: D029968:Escherichia coli Proteins; D029701:Saccharomyces cerevisiae Proteins