Tightening Causal Bounds via Covariate-Aware Optimal Transport
通过纳入协变量的最优传输收紧因果效应界AI 解读 ↓
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通过纳入协变量的最优传输收紧因果效应界
- 研究问题
- 当处理组与对照组潜在结果的联合关系未知时，如何利用协变量收紧因果参数的部分识别区间，并降低计算难度？
- 方法与思路
- 作者以带惩罚的松弛将条件最优传输转化为标准最优传输，保留协变量信息，并利用现有软件构造部分识别集估计量。
- 材料陈述的贡献
- 摘要称该松弛在任意惩罚参数下均能收紧区间，惩罚趋于无穷时渐近精确，并给出估计量的收敛速率与模拟比较。
- 阅读关注点
- 核对区间收紧的比较基准、松弛的有效性、惩罚参数如何随样本量变化，以及收敛速率所需的分布与协变量条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核实；摘要未说明具体因果参数、收敛速率及有限样本区间推断方法。
原文摘要
Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.