Causal inference is paramount for understanding the effects of interventions, yet extracting personalized insights from increasingly complex data remains a significant challenge for modern machine learning. This is the case, in particular, when considering functional outcomes observed over a continuous domain (e.g., time, or space). Estimation of heterogeneous treatment effects, known as CATE, has emerged as a crucial tool for personalized decision-making, but existing meta-learning frameworks are largely limited to scalar outcomes, failing to provide satisfying results in scientific applications that leverage the rich, continuous information encoded in functional data. Here, we introduce FOCaL (Functional Outcome Causal Learning), a novel, doubly robust meta-learner specifically engineered to estimate a functional heterogeneous treatment effect (F-CATE). FOCaL integrates advanced functional regression techniques for both outcome modeling and functional pseudo-outcome reconstruction, thereby enabling the direct and robust estimation of F-CATE. We provide a rigorous theoretical derivation of FOCaL, demonstrate its performance and robustness compared to existing non-robust functional methods through comprehensive simulation studies, and illustrate its practical utility on diverse real-world functional datasets. FOCaL advances the capabilities of machine intelligence to infer nuanced, individualized causal effects from complex data, paving the way for more precise and trustworthy AI systems in personalized medicine, adaptive policy design, and fundamental scientific discovery.

翻译：因果推断对于理解干预效应至关重要，然而从日益复杂的数据中提取个性化洞见仍然是现代机器学习面临的重大挑战。当考虑在连续域（例如时间或空间）上观测到的功能结果时，这一挑战尤为突出。异质处理效应（即CATE）的估计已成为个性化决策的关键工具，但现有的元学习框架主要局限于标量结果，无法在利用功能数据所编码的丰富连续信息的科学应用中提供令人满意的结果。本文提出FOCaL（功能结果因果学习），这是一种新颖的双重稳健元学习器，专门设计用于估计功能异质处理效应（F-CATE）。FOCaL集成了先进的功能回归技术，用于结果建模和功能伪结果重构，从而实现对F-CATE的直接且稳健的估计。我们提供了FOCaL的严格理论推导，通过全面的模拟研究证明了其相对于现有非稳健功能方法的性能和鲁棒性，并在多样化的真实世界功能数据集上展示了其实用价值。FOCaL提升了机器智能从复杂数据中推断细致入微的个体化因果效应的能力，为个性化医疗、适应性政策设计以及基础科学发现等领域中构建更精确、更可信赖的人工智能系统铺平了道路。