在单调性假设下，推导离散处理与有序结果的联合概率边界并实现识别。
Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions
- 提出新型单调性假设，将概率边界问题转化为线性规划。
- 通过新假设实现联合概率的完全识别，突破传统方法限制。
- 在真实数据集上验证方法有效性，适用于因果推断场景。
评估潜在结果与观测变量的联合概率及其线性组合，是因果推断中的基础挑战。本文研究离散处理与离散有序结果设定下的联合概率边界与识别问题。提出新的单调性假设家族，并将边界计算建模为线性规划问题。进一步引入一种新型单调性假设以实现概率的完全识别。最后通过数值实验验证方法有效性，并在真实数据集上展示其应用。结果表明，该框架可有效缩小概率不确定范围，并在特定条件下实现精确识别。
原文摘要 · Abstract (English)
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete ordinal outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.
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