Identifying the causal relationship among variables from observational data is an important yet challenging task. This work focuses on identifying the direct causes of an outcome and estimating their magnitude, i.e., learning the causal outcome model. Data from multiple environments provide valuable opportunities to uncover causality by exploiting the invariance principle that the causal outcome model holds across heterogeneous environments. Based on the invariance principle, we propose the Negative Weighted Distributionally Robust Optimization (NegDRO) framework to learn an invariant prediction model. NegDRO minimizes the worst-case combination of risks across multiple environments and enforces invariance by allowing potential negative weights. Under the additive interventions regime, we establish three major contributions: (i) On the statistical side, we provide sufficient and nearly necessary identification conditions under which the invariant prediction model coincides with the causal outcome model; (ii) On the optimization side, despite the nonconvexity of NegDRO, we establish its benign optimization landscape, where all stationary points lie close to the true causal outcome model; (iii) On the computational side, we develop a gradient-based algorithm that provably converges to the causal outcome model, with non-asymptotic convergence rates in both sample size and gradient-descent iterations. In particular, our method avoids exhaustive combinatorial searches over exponentially many subsets of covariates found in the literature, ensuring scalability even when the dimension of the covariates is large. To our knowledge, this is the first causal invariance learning method that finds the approximate global optimality for a nonconvex optimization problem efficiently.

翻译：从观测数据中识别变量间的因果关系是一项重要而具有挑战性的任务。本研究聚焦于识别结果变量的直接原因并估计其影响强度，即学习因果结果模型。来自多个环境的数据为揭示因果关系提供了宝贵机会，其核心在于利用因果结果模型在异质环境中保持不变的不变性原理。基于该原理，我们提出负加权分布鲁棒优化（NegDRO）框架来学习不变预测模型。NegDRO通过最小化多环境风险的最坏组合，并允许潜在负权重来强制实现不变性。在加性干预机制下，我们取得三方面主要贡献：（i）在统计层面，我们建立了充分且近乎必要的可识别条件，使得不变预测模型与因果结果模型相一致；（ii）在优化层面，尽管NegDRO具有非凸性，我们证明了其良好的优化景观——所有平稳点均接近真实因果结果模型；（iii）在计算层面，我们开发了基于梯度的算法，该算法可证明收敛至因果结果模型，并在样本量和梯度下降迭代次数上均具有非渐近收敛速率。特别地，本方法避免了文献中对协变量指数级子集进行穷举组合搜索的过程，确保即使在高维协变量场景下仍具有可扩展性。据我们所知，这是首个能高效求解非凸优化问题近似全局最优解的因果不变性学习方法。