Discovering causal relationships from observational data is a fundamental yet challenging task. In some applications, it may suffice to learn the causal features of a given response variable, instead of learning the entire underlying causal structure. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings. ICP assumes that the mechanism for generating the response from its direct causes is the same in all settings and exploits this invariance to output a subset of the causal features. The framework of ICP has been extended to general additive noise models and to nonparametric settings using conditional independence testing. However, nonparametric conditional independence testing often suffers from low power (or poor type I error control) and the aforementioned parametric models are not suitable for applications in which the response is not measured on a continuous scale, but rather reflects categories or counts. To bridge this gap, we develop ICP in the context of transformation models (TRAMs), allowing for continuous, categorical, count-type, and uninformatively censored responses (we show that, in general, these model classes do not allow for identifiability when there is no exogenous heterogeneity). We propose TRAM-GCM, a test for invariance of a subset of covariates, based on the expected conditional covariance between environments and score residuals which satisfies uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we propose an additional invariance test, TRAM-Wald, based on the Wald statistic. We implement both proposed methods in the open-source R package "tramicp" and show in simulations that under the correct model specification, our approach empirically yields higher power than nonparametric ICP based on conditional independence testing.

翻译：从观测数据中发现因果关系是一项基础但具有挑战性的任务。在某些应用中，仅需学习给定响应变量的因果特征，而非整个潜在因果结构。不变因果预测（ICP, Peters et al., 2016）是一种因果特征选择方法，要求数据来自异质环境。ICP假设所有环境中响应变量从其直接原因生成的机制相同，并利用这一不变性输出因果特征子集。ICP框架已通过条件独立性检验扩展到一般加性噪声模型和非参数设置。然而，非参数条件独立性检验通常功效较低（或第一类错误控制较差），且上述参数模型不适用于响应变量非连续尺度测量（而是反映类别或计数）的应用。为弥合这一差距，我们在转换模型（TRAMs）框架下开发ICP，允许处理连续型、类别型、计数型和无信息删失型响应（我们表明，通常当不存在外生异质性时，这些模型类不允许可识别性）。我们提出TRAM-GCM，一种基于环境与得分残差之间的期望条件协方差来检验协变量子集不变性的方法，该方法满足均匀渐近水平保证。针对线性移位TRAM的特殊情况，我们提出另一种基于Wald统计量的不变性检验TRAM-Wald。我们在开源R包"tramicp"中实现了这两种方法，并通过模拟表明，在正确模型设定下，我们的方法经验地在功效上优于基于条件独立性检验的非参数ICP。