针对分类处理变量的个体化治疗规则的部分识别学习
Partial Identification Learning with Categorical Treatments for Individualized Treatment Rules
AI总结：
该研究针对分类处理等变量，扩展了部分识别学习框架，提出广义极小极大损失准则与对称嵌入策略，所得个体化治疗规则在未测量混杂场景中更接近最优规则。
AI中文摘要：
我们开发了一个针对个体化治疗规则（ITR）的部分识别学习框架，该框架适用于分类处理变量、结局变量和工具变量。与依赖点识别所需的强因果假设不同，我们的框架利用因果界来刻画最优治疗决策。现有的部分识别下ITR优化方法大多局限于二元处理设置，以及Balke和Pearl在经典工具变量设计下推导的界。我们将该框架扩展以适应更广泛的因果结构，以及处理变量、结局变量和工具变量均为分类变量的场景。我们引入了一种广义极小极大损失准则，用于从两个以上选项中选择治疗方案，该准则基于部分识别界最小化所选治疗与最优治疗之间的最大可能差异。为构建ITR，我们采用对称嵌入策略，将离散处理变量映射到正则单纯形的顶点，避免了标准一对其余方法的几何不一致性。我们推导了一个可微的加权代理风险函数，并证明优化该函数可解决原始问题。此外，我们在一般正则性条件下通过oracle不等式提供了有限样本收敛率，我们证明基于核的实现满足这些条件。数值实验表明，在存在未测量混杂的场景中，该框架生成的ITR与现有替代方法相比，显著更接近oracle ITR。
英文摘要：
We develop a partial identification learning framework for individualized treatment rules (ITRs) with categorical treatments, outcomes, and instrumental variables. Rather than relying on strong causal assumptions required for point identification, our framework leverages causal bounds to characterize the optimal treatment decision. Existing methods for ITR optimization under partial identification are largely restricted to binary treatment settings and the bounds derived by Balke and Pearl under the canonical instrumental variable design. We extend this framework to accommodate a broader class of causal structures as well as scenarios with categorical treatment, outcome, and instrumental variables. We introduce a generalized minimax loss criterion for treatment selection from among more than two options, which minimizes the maximum possible difference between the chosen and the optimal treatment based on partial identification bounds. To construct the ITR, we use a symmetric embedding strategy that maps discrete treatments to the vertices of a regular simplex, avoiding the geometric inconsistencies of standard one-vs-rest approaches. We derive a differentiable, weighted surrogate risk function and show that optimizing it solves the original problem. Furthermore, we provide finite sample convergence rates via an oracle inequality under general regularity conditions, which we show are satisfied by a kernel based implementation. Numerical experiments demonstrate that the framework yields ITRs significantly closer to the oracle ITR compared to existing alternatives in settings with unmeasured confounding.
