It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution shifts. One principled approach is to adopt the structural causal models to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle might be violated in practical settings when the response is intervened. A natural question is whether it is still possible to identify other forms of invariance to facilitate prediction in unseen environments. To shed light on this challenging scenario, we focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP), an explicit relation to capture interventions through an additional feature, leading to an alternative form of invariance that enables a unified treatment of general interventions on the response as well as the predictors. We analyze the asymptotic generalization errors of our method under both the discrete and continuous environment settings, where the continuous case is handled by relating it to the semiparametric varying coefficient models. We present algorithms that show competitive performance compared to existing methods over various experimental settings including a COVID dataset.

翻译：如今，在不同环境中收集特征与响应配对观测数据的情况日益普遍。因此，由于分布偏移，需将已习得的预测模型应用于具有不同分布的数据。一种原则性方法是采用结构因果模型描述训练与测试模型，并遵循不变性原则——该原则指出，在跨环境中响应给定预测变量的条件分布保持不变。然而，当响应本身受到干预时，这一原则在实际场景中可能被违反。一个自然的问题是：是否仍能识别其他形式的不变性，以促进在未见环境中的预测？为阐明这一具有挑战性的场景，我们聚焦于线性结构因果模型，并引入不变匹配性质——通过额外特征捕获干预的显式关系，从而形成一种替代形式的不变性，使得能够统一处理对响应及预测变量的广义干预。我们分析了该方法在离散与连续环境设置下的渐近泛化误差，其中连续情况通过将其与半参数变系数模型关联进行处理。我们提出的算法在多种实验设置（包括COVID数据集）中展现出与现有方法相比具有竞争力的性能。