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.

本文提出了一种基于因果性的分布鲁棒性方法，命名为分布鲁棒性通过不变梯度（DRIG），通过利用训练数据中的一般加性干预来实现对未见干预的鲁棒预测，自然地在分布预测和因果性之间插值。在线性设置中，证明DRIG在数据相关的一类分布转换中得到鲁棒的预测。此外，还扩展了该方法到半监督领域适应设置以进一步提高预测性能。最后，通过合成模拟和单细胞数据对我们的方法进行了实证验证。

因果导向的鲁棒性: 利用一般性可加介入