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arXiv 2010.02247stat.MEcs.IRcs.ITmath.ITnlin.CD
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不可干预系统中的因果发现框架

A Framework for Causal Discovery in non-intervenable systems

Peter Jan van Leeuwen, Michael DeCaria, Nachiketa Chakaborty, Manuel Pulido

摘要:

在复杂的非线性系统中,存在许多框架来推断因果关系,但缺乏一个完整的理论。提出了一个新的框架,是完全非线性的,提供了一个完整的信息理论解开因果过程,允许非线性的原因之间的相互作用,确定缺失或未知的过程的因果强度,并可以分析系统,不能表示有向无环图。基本的构建块是信息理论的措施,如(条件)互信息和一个新的概念,称为确定性,单调增加的信息有关的目标进程。详细介绍了该框架,并与其他现有的框架进行了比较,并讨论了混杂因素的处理。虽然有系统的结构,框架不能解开,有人认为,任何因果框架,是基于集成量将错过潜在的重要信息的潜在概率密度函数。该框架在几个高度简化的随机过程上进行了测试,以演示如何处理阻塞和网关,以及混沌Lorentz 1963系统。我们表明,该框架提供了信息的本地动态,但也揭示了更大规模的结构的基础吸引子的信息。此外,通过将其应用到与厄尔尼诺南方振荡系统相关的实际观测中,我们证明了其相对于其他方法的能力和优势。

英文摘要:

Many frameworks exist to infer cause and effect relations in complex nonlinear systems but a complete theory is lacking. A new framework is presented that is fully nonlinear, provides a complete information theoretic disentanglement of causal processes, allows for nonlinear interactions between causes, identifies the causal strength of missing or unknown processes, and can analyze systems that cannot be represented on Directed Acyclic Graphs. The basic building blocks are information theoretic measures such as (conditional) mutual information and a new concept called certainty that monotonically increases with the information available about the target process. The framework is presented in detail and compared with other existing frameworks, and the treatment of confounders is discussed. While there are systems with structures that the framework cannot disentangle, it is argued that any causal framework that is based on integrated quantities will miss out potentially important information of the underlying probability density functions. The framework is tested on several highly simplified stochastic processes to demonstrate how blocking and gateways are handled, and on the chaotic Lorentz 1963 system. We show that the framework provides information on the local dynamics, but also reveals information on the larger scale structure of the underlying attractor. Furthermore, by applying it to real observations related to the El-Nino-Southern-Oscillation system we demonstrate its power and advantage over other methodologies.

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