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：我们提出了一种因果正则化的锚点回归扩展方法，以提升分布外泛化能力。我们引入了与锚点框架兼容的损失函数，确保对分布偏移的鲁棒性。多种多元分析算法，如(正交化的)偏最小二乘、降秩回归和多元线性回归，均属于锚点框架范畴。我们发现，简单的正则化即可增强分布外环境下的鲁棒性。针对所选算法给出了估计量，在合成问题和现实气候科学问题中验证了一致性与有效性。实证结果凸显了锚点正则化的多功能性，强调了其与多元分析算法的兼容性，以及在抵抗分布偏移的同时提升可复制性的作用。扩展后的锚点回归框架推进了因果推断方法论，满足了可靠分布外泛化的需求。