标题： 因果模型中的鲁棒优化和G-因果归一化流 显示英文标题

标题： Robust Optimization in Causal Models and G-Causal Normalizing Flows

摘要： 在本文中，我们表明，在因果模型中的干预鲁棒优化问题在$G$-因果 Wasserstein 距离下是连续的，但在标准 Wasserstein 距离下可能不连续。这突出了在为这类任务增强数据时使用尊重因果结构的生成模型的重要性。为此，我们提出了一种新的归一化流架构，该架构满足因果结构模型的通用逼近性质，并可以高效地训练以最小化$G$-因果 Wasserstein 距离。实证上，我们展示了我们的模型在因果回归和因果因子模型中的均值-方差投资组合优化的数据增强任务中优于标准（非因果）生成模型。 显示英文摘要

摘要： In this paper, we show that interventionally robust optimization problems in causal models are continuous under the $G$-causal Wasserstein distance, but may be discontinuous under the standard Wasserstein distance. This highlights the importance of using generative models that respect the causal structure when augmenting data for such tasks. To this end, we propose a new normalizing flow architecture that satisfies a universal approximation property for causal structural models and can be efficiently trained to minimize the $G$-causal Wasserstein distance. Empirically, we demonstrate that our model outperforms standard (non-causal) generative models in data augmentation for causal regression and mean-variance portfolio optimization in causal factor models.