Since distribution shifts are common in real-world applications, there is a pressing need for developing prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general additive interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. Furthermore, we show that our framework includes anchor regression (Rothenh\"ausler et al.\ 2021) as a special case, and that it yields prediction models that protect against more diverse perturbations. We extend our approach to the semi-supervised domain adaptation setting to further improve prediction performance. Finally, we empirically validate our methods on synthetic simulations and on single-cell data.

翻译：由于分布偏移在现实应用中普遍存在，亟需开发对这类偏移具有鲁棒性的预测模型。现有框架（如经验风险最小化或分布鲁棒优化）要么对新分布缺乏泛化能力，要么依赖于人为假定的距离度量。因果性为鲁棒预测提供了数据驱动且结构化的视角，但因果推断所需的假设可能过于严格，且此类因果模型提供的鲁棒性往往缺乏灵活性。本文聚焦于面向因果的鲁棒性，提出基于不变梯度的分布鲁棒方法（DRIG），该方法利用训练数据中的广义加性干预实现针对未见干预的鲁棒预测，并自然地在同分布预测与因果性之间平滑过渡。在线性设定下，我们证明DRIG能在数据依赖性分布偏移类中生成鲁棒预测。进一步表明，该框架包含锚定回归（Rothenhäusler等，2021）作为特例，并能产生抵御更多样化扰动的预测模型。我们将方法扩展至半监督域适应场景以提升预测性能，最终在合成仿真数据和单细胞数据上进行了实验验证。