方法对比

	转移熵	收敛交叉映射 (CCM)	样本熵
领域	因果推断	因果推断	复杂系统
方法族	Machine learning	Machine learning	Machine learning
起源年份	2000	2012	2000
提出者	Thomas Schreiber	George Sugihara et al.	Richman & Moorman
类型	Non-parametric information-theoretic measure	Nonlinear time-series causality test	Nonlinear entropy measure
开创性文献	Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.	Sugihara, G., et al. (2012). Detecting causality in complex ecosystems. Science, 338(6106), 496–500.	Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology, 278(6), H2039–H2049.
别名	Schreiber Information Transfer, Directed Information Flow, Conditional Mutual Information (directed), Transfer Entropisi	CCM, Cross-Convergent Mapping, Empirical Dynamic Modelling Causality, Yakınsak Çapraz Haritalama	SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
相关	3	3	2
摘要	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.	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.	Sample Entropy (SampEn) is a nonlinear measure of the complexity and regularity of a time series. Introduced by Richman and Moorman in 2000 as an improvement over Approximate Entropy (ApEn), it quantifies the likelihood that similar patterns of a given length in the series remain similar when extended by one additional data point. A higher SampEn value indicates greater irregularity and complexity, while a lower value indicates more regularity or self-similarity.