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arXiv 2001.06208stat.MEmath.DS
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动力系统的因果模型

Causal models for dynamical systems

Jonas Peters, Stefan Bauer, Niklas Pfister

摘要:

概率模型描述了处于观测状态的系统。然而,在许多情况下,我们感兴趣的是系统在干预下的反应。结构因果模型类提供了一种语言,使我们能够对干预下的行为进行建模。它可以作为一个起点来回答大量的因果问题,包括因果效应的识别或因果结构学习。在这一章中,我们提供了一个自然的和直接的扩展这个概念的动力系统,专注于连续时间模型。特别是,我们介绍了两种类型的因果动力学模型,不同的随机性如何进入模型:它可以被认为是观测噪声或系统驱动噪声。在这两种情况下,我们都定义了干预措施,因此为因果推断提供了可能的起点。从这个意义上说,本书提供的问题多于答案。例如,所提出的因果动力学模型的重点在于动力学本身,而不是相应的平稳分布。我们认为,当目标是对系统的全时演变进行建模并且在不同时间点测量数据时,这是有益的。在这个焦点下,考虑微分方程本身的干预是很自然的。

英文摘要:

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to model the behaviour under interventions. It can been taken as a starting point to answer a plethora of causal questions, including the identification of causal effects or causal structure learning. In this chapter, we provide a natural and straight-forward extension of this concept to dynamical systems, focusing on continuous time models. In particular, we introduce two types of causal kinetic models that differ in how the randomness enters into the model: it may either be considered as observational noise or as systematic driving noise. In both cases, we define interventions and therefore provide a possible starting point for causal inference. In this sense, the book chapter provides more questions than answers. The focus of the proposed causal kinetic models lies on the dynamics themselves rather than corresponding stationary distributions, for example. We believe that this is beneficial when the aim is to model the full time evolution of the system and data are measured at different time points. Under this focus, it is natural to consider interventions in the differential equations themselves.

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