Structural Causal Models: Cycles, Marginalizations, Exogenous Reparametrizations and Reductions
Structural Causal Models: Cycles, Marginalizations, Exogenous Reparametrizations and Reductions
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结构因果模型：循环、边缘化、外生重参数化和归约
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发表时间：
2016
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通讯作者：
J. Mooij
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作者：
S. Bongers;J. Peters;B. Scholkopf;J. Mooij
结构因果模型（SCMs），也被称为非参数结构方程模型（NP - SEMs），被广泛用于因果建模目的。在本文中，我们对结构因果模型进行了严格的处理，解决了在存在循环关系时出现的测度理论复杂性问题。本文研究的核心问题是：给定一个在一个大系统（由可观测的内生变量和潜在的外生变量组成）上定义的（可能是循环的）结构因果模型，我们能否将其“投影”到一个描述子系统（由观测到的内生变量的一个子集以及可能不同的潜在外生变量组成）的结构因果模型上，以便获得该子系统的一种更简约但等价的表示呢？我们定义了一种边缘化操作，它能有效地从模型中移除一部分内生变量，以及一类映射，即外生重新参数化，它可用于减少外生变量的空间。我们表明这两种操作都保留了模型的因果语义，并且在温和的条件下，它们至少在模型变量数量方面能够显著降低模型的复杂性。我们认为，对于从数据中估计结构因果模型的任务，“平滑”约简的存在是可取的。我们提供了几个可以证明这种约简存在的条件，但也提供了一个反例，表明这种约简一般并不存在。后一个结果意味着从数据中估计线性或马尔可夫结构因果模型的现有方法不能扩展到一般的结构因果模型。
Structural causal models (SCMs), also known as non-parametric structural equation models (NP-SEMs), are widely used for causal modeling purposes. In this paper, we give a rigorous treatment of structural causal models, dealing with measure-theoretic complications that arise in the presence of cyclic relations. The central question studied in this paper is: given a (possibly cyclic) SCM defined on a large system (consisting of observable endogenous and latent exogenous variables), can we "project it down" to an SCM that describes a subsystem (consisting of a subset of the observed endogenous variables and possibly different latent exogenous variables) in order to obtain a more parsimonious but equivalent representation of the subsystem? We define a marginalization operation that effectively removes a subset of the endogenous variables from the model, and a class of mappings, exogenous reparameterizations, that can be used to reduce the space of exogenous variables. We show that both operations preserve the causal semantics of the model and that under mild conditions they can lead to a significant reduction of the model complexity, at least in terms of the number of variables in the model. We argue that for the task of estimating an SCM from data, the existence of "smooth" reductions would be desirable. We provide several conditions under which the existence of such reductions can be shown, but also provide a counterexample that shows that such reductions do not exist in general. The latter result implies that existing approaches to estimate linear or Markovian SCMs from data cannot be extended to general SCMs.