手法を比較

	収束的相互写像（CCM）	再帰定量化解析 (RQA)	Transfer Entropy
分野	因果推論	複雑系	因果推論
系統	Machine learning	Machine learning	Machine learning
提唱年	2012	2007	2000
提唱者	George Sugihara et al.	Marwan, Romano, Thiel & Kurths	Thomas Schreiber
種類	Nonlinear time-series causality test	Nonlinear time-series characterization	Non-parametric information-theoretic measure
原典	Sugihara, G., et al. (2012). Detecting causality in complex ecosystems. Science, 338(6106), 496–500.	Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329.	Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.
別名	CCM, Cross-Convergent Mapping, Empirical Dynamic Modelling Causality, Yakınsak Çapraz Haritalama	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi	Schreiber Information Transfer, Directed Information Flow, Conditional Mutual Information (directed), Transfer Entropisi
関連	3	2	3
概要	Convergent Cross Mapping (CCM) is a nonlinear, state-space method for detecting causality between time-series variables embedded in a shared dynamical system. Introduced by George Sugihara and colleagues in their landmark 2012 Science paper, CCM exploits Takens' embedding theorem: if variable X causally influences Y, the historical record of Y contains enough information to recover the states of X. Causality is confirmed when cross-map skill improves—converges—as the time-series library grows longer.	Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems.	Transfer Entropy (TE) is a non-parametric, information-theoretic measure of directed statistical dependence between two time series, introduced by Thomas Schreiber in 2000. Grounded in Shannon entropy, it quantifies how much information the past of one process Y reduces uncertainty about the next state of another process X, beyond what X's own past already provides. Unlike linear correlation or Granger causality, TE captures nonlinear interactions and requires no model assumptions about the underlying dynamics.