Partial Identification under Causal Orders by Linear Programming

2026-08-25

AI Summary

该研究通过线性编程方法，利用因果顺序对反事实查询进行部分识别，解决了在领域知识不完整情况下的非参数识别问题。

Abstract

Non-parametric (partial) identification of counterfactual queries typically relies on a fully specified causal graph. Motivated by settings with incomplete domain knowledge, we challenge this requirement by leveraging structural assumptions that are inherently implied by the query itself. We show that any counterfactual inquiry induces a, mostly partial, topological ordering over relevant variables, which, in turn, enables an explicit query parametrisation reducing the identification task to a linear program. This allows bounding arbitrary counterfactual and nested counterfactual queries. Our work can be viewed as a generalisation of the classical bounding framework of Tian and Pearl (2000), originally developed for probabilities of causation. We also prove the \emph{tightness} of our bounds by constructing structural causal models that attain the bounds whilst being compatible with both the observed data and the query-implied order. To assess both the generality and practical utility of the proposed bounding procedure, we revisit several case studies from the literature, demonstrating how the derived bounds can be used to yield informative insights even in the absence of an input causal graph.

Problem

• partial identification
• counterfactual queries
• causal orders
• linear programming
• structural assumptions

Innovation

• partial identification
• causal orders
• linear programming
• counterfactual queries
• topological ordering