Abstract An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system’s underlying causal structure. To this end, Invariant Causal Prediction (ICP) [1] has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence. In this work, we present and evaluate an array of methods for nonlinear and nonparametric versions of ICP for learning the causal parents of given target variables. We find that an approach which first fits a nonlinear model with data pooled over all environments and then tests for differences between the residual distributions across environments is quite robust across a large variety of simulation settings. We call this procedure “invariant residual distribution test”. In general, we observe that the performance of all approaches is critically dependent on the true (unknown) causal structure and it becomes challenging to achieve high power if the parental set includes more than two variables. As a real-world example, we consider fertility rate modeling which is central to world population projections. We explore predicting the effect of hypothetical interventions using the accepted models from nonlinear ICP. The results reaffirm the previously observed central causal role of child mortality rates.

中文翻译：

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非线性模型的不变因果预测

摘要 许多领域的一个重要问题是预测系统将如何响应干预。这项任务与估计系统的潜在因果结构有着内在的联系。为此，已经提出了不变因果预测 (ICP) [1]，它使用来自不同环境的数据来学习利用因果关系不变性的因果模型。在考虑线性模型时，ICP 的实现相对简单。然而，由于条件独立性的非参数检验的难度，非线性情况更具挑战性。在这项工作中，我们提出并评估了一系列用于学习给定目标变量的因果父对象的非线性和非参数版本的 ICP 方法。我们发现，一种首先使用在所有环境中汇集的数据拟合非线性模型，然后测试跨环境残差分布之间差异的方法在各种模拟设置中都非常稳健。我们称这个过程为“不变残差分布测试”。总的来说，我们观察到所有方法的性能都严重依赖于真实（未知）因果结构，如果父集包含两个以上的变量，实现高功率就变得具有挑战性。作为一个现实世界的例子，我们考虑生育率模型，它是世界人口预测的核心。我们探索使用来自非线性 ICP 的公认模型来预测假设干预的效果。结果重申了先前观察到的儿童死亡率的核心因果作用。