基于经验动态建模的因果检测研究综述

Review on Causality Detection Based on Empirical Dynamic Modeling

相关性是目前科学研究中重要的分析标准,但是相关关系并不意味着因果关系。随着人们认识到非线性动力学的普遍性,仅仅依靠相关性进行推论,极有可能会得出错误的结论。目前,包括机器学习在内的各种相关性研究算法快速发展,而挖掘变量间因果关联的研究尚处于探索中。经验动态建模理论是一种基于数据驱动的动态系统建模框架,其最大的特点是抛弃了传统数据分析中的公式化方法,仅仅从时间序列中重构动态系统的行为。其核心思想是动态系统可以描述为一组状态在高维空间中受一定规则的驱使随时间演变的过程,可以通过重建随时间演变的状态来对动态系统进行建模。基于经验动态建模理论,通过动态系统中变量的时序数据,可以对变量之间的因果关系进行检测。如果变量X是变量Y的原因(X⇒Y),那么变量X的信息必须隐含在变量Y中,且可以从变量Y中恢复。文中首先分析了相关性与因果关系的辩证关系,由于“虚假相关性”和“幻象性相关”现象的存在,相关性并不意味着因果性,缺乏相关性也并不意味着没有因果关联;然后全面介绍基于经验动态建模理论进行因果检测的核心思想,具体地对Takens嵌入定理、单纯形投影算法和收敛交叉映射算法的历史发展做了详细总结,动态系统可以描述为一组状态在高维空间中受一定规则的驱使随时间演变的过程,可以通过重建随时间演变的状态来对动态系统进行建模;接着介绍了一些经验动态建模理论改进方法和实际因果检测应用;最后分析了基于经验动态建模因果检测目前存在的一些问题,并对未来发展趋势进行了展望。

Correlation is an important analysis standard in curent scientific research,but it does not mean causality.As people rea-lize the universality of no nlinear dynamics,it is very likely to lead to wrong conclusions only by relying on corelation.At present,various correlation research algorithms,including machine learning,are developing rapidly,while the research of mining causal correlation between variables is still under exploration.Empirical dynamic modeling theory is a data-driven dynamic system mo-deling framework.Its biggest feature is to abandon the formulaic method in traditional data analysis and reconstruct the behavior of dynamic system only from time series.The core idea is that a dynamic system can be described as a process in which a group of states evolve over time driven by certain rules in high-dimensional space.The dynamic system can be modeled by reconstructing the states that evolve over time.Based on empirical dynamic modeling theory,the causal relationship betwen variables can be detected through the time series data of variables in dynamic system.If variable X is the cause of variable Y(X⇒Y),the information of variable X must be implicit in variable Y and can be recovered from variable Y.This paper first analyzes the dialectical relationship between correlation and causality.Correlation does not mean causality,and lack of correlation does not mean no causality.Then it comprehensively introduces the core idea of causality detection based on empirical dynamic modeling theory,andsummarizes the historical development of Takens embedding theorem,simplex projection algorithm and convergent cross mapping algorithm.It introduces some improved methods of empirical dynamic modeling theory and practical application of causal detection,and finaly looks forward to the future development trend of causal detection based on empirical dynamic modeling.