We introduce a causal regularisation extension to anchor regression (AR) for improved out-of-distribution (OOD) generalisation. We present anchor-compatible losses, aligning with the anchor framework to ensure robustness against distribution shifts. Various multivariate analysis (MVA) algorithms, such as (Orthonormalized) PLS, RRR, and MLR, fall within the anchor framework. We observe that simple regularisation enhances robustness in OOD settings. Estimators for selected algorithms are provided, showcasing consistency and efficacy in synthetic and real-world climate science problems. The empirical validation highlights the versatility of anchor regularisation, emphasizing its compatibility with MVA approaches and its role in enhancing replicability while guarding against distribution shifts. The extended AR framework advances causal inference methodologies, addressing the need for reliable OOD generalisation.

我们通过引入因果正则化扩展到锚定回归（AR）来改善超出分布的广义。我们提出与锚定框架一致的锚定兼容损失，以确保对分布变化的鲁棒性。各种多变量分析（MVA）算法，如（正交化）PLS，RRR和MLR，都适用于锚定框架。我们观察到简单的正则化能增强在超出分布设置下的鲁棒性。我们提供了选择算法的估计器，展示了它们在合成和真实的气候科学问题中的一致性和功效。经验证实，锚定正则化的通用性凸显了其与MVA方法的兼容性，并在增强可复制性的同时防范了分布变化。扩展的AR框架推进了因果推断方法，解决了可靠的超出分布广义化的需求。

通过锚定多元分析提高泛化能力