Making predictions in an unseen environment given data from multiple training
environments is a challenging task. We approach this problem from an invariance
perspective, focusing on binary classification to shed light on general
nonlinear data generation mechanisms. We identify a unique form of invariance
that exists solely in a binary setting that allows us to train models invariant
over environments. We provide sufficient conditions for such invariance and
show it is robust even when environmental conditions vary greatly. Our
formulation admits a causal interpretation, allowing us to compare it with
various frameworks. Finally, we propose a heuristic prediction method and
conduct experiments using real and synthetic datasets.

在多个训练环境中给出数据的情况下，如何在未知环境中进行预测是一项具有挑战性的任务。我们从不变性的角度来解决这个问题，着重研究二元分类以揭示一般非线性的数据生成机制。我们发现了一种仅存在于二元情况下的独特不变性形式，使我们能够训练在不同环境中都保持不变的模型。我们提供了这种不变性的充分条件，并证明在环境条件变化很大的情况下它是稳健的。我们的建模方法允许有因果解释，使我们能够将其与各种框架进行比较。最后，我们提出了一种基于启发式的预测方法，并使用真实和合成数据集进行了实验。