Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenhäusler et al. (J R Stat Soc Ser B 83(2):215–246, 2021. https://doi.org/10.1111/rssb.12398), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.

如果训练和测试数据不是来自同一分布，预测模型通常会失败。对看不见的、受扰动的测试数据的分布外 (OOD) 泛化是预测模型的理想但难以实现的属性，并且通常需要对数据生成过程 (DGP) 做出强有力的假设。从对 OOD 泛化的因果启发的角度来看，测试数据来自对 DGP 的外生随机变量（称为锚点）的特定干预类别。锚回归模型，由 Rothenhäusler 等人介绍。（JR Stat Soc Ser B 83(2):215–246, 2021. https://doi.org/10.1111/rssb.12398）通过采用因果正则化来防止测试数据的分布变化。然而，到目前为止，锚回归仅用于平方误差损失，这不适用于常见的响应，例如删失的连续或有序数据。在这里，我们提出了锚回归的分布版本，该版本将该方法推广到至少具有有序样本空间的潜在审查响应。为此，我们在更一般的残差概念下将用于分布回归的一类灵活的参数变换模型与适当的因果正则化器相结合。在一个示例性应用程序和几个模拟场景中，我们展示了 OOD 泛化的可能程度。我们在更一般的残差概念下将用于分布回归的一类灵活的参数转换模型与适当的因果正则化器相结合。在一个示例性应用程序和几个模拟场景中，我们展示了 OOD 泛化的可能程度。我们在更一般的残差概念下将用于分布回归的一类灵活的参数转换模型与适当的因果正则化器相结合。在一个示例性应用程序和几个模拟场景中，我们展示了 OOD 泛化的可能程度。