One of the basic aims of science is to unravel the chain of cause and effect of particular systems. Especially for large systems, this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to resolve the causality question, but for many systems, such interventions are impossible or too costly to obtain. Recently, Maathuis et al. (2010), following ideas from Spirtes et al. (2000), introduced a framework to estimate causal effects in large scale Gaussian systems. By describing the causal network as a directed acyclic graph it is a possible to estimate a class of Markov equivalent systems that describe the underlying causal interactions consistently, even for non-Gaussian systems. In these systems, causal effects stop being linear and cannot be described any more by a single coefficient. In this paper, we derive the general functional form of a causal effect in a large subclass of non-Gaussian distributions, called the non-paranormal. We also derive a convenient approximation, which can be used effectively in estimation. We show that the estimate is consistent under certain conditions and we apply the method to an observational gene expression dataset of the Arabidopsis thaliana circadian clock system.

中文翻译：

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从非超自然观测数据估计因果效应。

科学的基本目标之一是解开特定系统的因果链。特别是对于大型系统，这可能是一项艰巨的任务。详细的干预和随机数据采样方法可用于解决因果关系问题，但是对于许多系统而言，此类干预是不可能的，或者获取成本太高。最近，Maathuis等。（2010年），遵循Spirtes等人的想法。（2000年），引入了一个框架来估计大规模高斯系统中的因果效应。通过将因果网络描述为有向无环图，可以估计一类马尔可夫等效系统，即使对于非高斯系统，该系统也能一致地描述潜在的因果相互作用。在这些系统中，因果关系不再是线性的，无法再用单个系数来描述。在本文中，我们在非高斯分布的大子类中推导了因果效应的一般函数形式，称为非超自然现象。我们还导出了一个方便的近似，可以将其有效地用于估计。我们表明估计值在某些条件下是一致的，我们将该方法应用于拟南芥生物钟系统的观测基因表达数据集。