Partial Identification Learning with Categorical Treatments for Individualized Treatment Rules

2026-08-20

AI Summary

本文提出了一种针对分类处理、结果和工具变量的个性化治疗规则的部分识别学习框架，通过因果界限而非强因果假设来确定最优治疗决策，并引入了广义最小最大损失标准。

Abstract

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.

Problem

• individualized treatment rules
• partial identification
• categorical treatments

Innovation

• partial identification learning
• categorical treatments
• generalized minimax loss
• symmetric embedding strategy
• causal bounds