Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant'' in some sense.However, these methods generally contradict each other, and none of them consistently improve performance on real-world domain shift benchmarks. There are two main questions that must be addressed to understand when, if ever, we should use each method. First, how does each ad hoc notion of ``invariance'' relate to the structure of real-world problems? And, second, when does learning invariant representations actually yield robust models? To address these issues, we introduce a broad formal notion of what it means for a real-world domain shift to admit invariant structure. Then, we characterize the causal structures that are compatible with this notion of invariance.With this in hand, we find conditions under which method-specific invariance notions correspond to real-world invariant structure, and we clarify the relationship between invariant structure and robustness to domain shifts. For both questions, we find that the true underlying causal structure of the data plays a critical role.

翻译：机器学习方法在部署于与训练数据不同领域时可能不可靠。已有大量方法通过学习某种意义上的“不变”表示来缓解这一问题，但这些方法往往相互矛盾，且均未能在真实域移位基准上持续提升性能。要理解在何种情况下（如果存在）应使用每种方法，需解决两个关键问题：第一，每种特定的“不变性”概念如何与真实问题的结构相关联？第二，学习不变表示何时能真正产生鲁棒模型？为解答这些问题，我们提出了一个广义形式化定义，描述真实域移位允许存在不变结构的必要条件。随后，我们刻画了与这种不变性概念兼容的因果结构。基于此，我们找到了特定方法的不变性概念对应真实世界不变结构的条件，并阐明了不变结构与域移位鲁棒性之间的关系。针对这两个问题，我们发现数据真实的潜在因果结构起着关键作用。