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.

翻译：我们提出了一种锚定回归（AR）的因果正则化扩展方法，以提升分布外（OOD）泛化能力。我们引入了与锚定框架兼容的损失函数，确保对分布偏移具有鲁棒性。多种多元分析（MVA）算法，如（正交标准化）偏最小二乘（PLS）、降秩回归（RRR）和多元线性回归（MLR），均隶属于锚定框架。我们观察到，简单的正则化能增强OOD场景下的鲁棒性。本文给出了选定算法的估计量，在合成数据及真实气候科学问题中展示了其一致性与有效性。实证验证凸显了锚定正则化的普适性，强调了其与MVA方法的兼容性，以及在增强可复现性同时抵御分布偏移的作用。扩展后的AR框架推进了因果推断方法论，满足了可靠OOD泛化的需求。