用动态最优传输理论解决高维因果反事实可识别性问题
Counterfactual Identifiability via Dynamic Optimal Transport
- 基于连续时间流模型构建反事实传输映射
- 在真实图像数据上实现更可靠的反事实推断
- 适用于需要严格因果验证的研究者
我们解决了从观测数据中对高维多变量结果进行反事实识别的开放问题。Pearl（2000）指出，反事实必须可识别（即能从观测数据分布中恢复），才能支撑因果推断。近期反事实推断研究虽有进展，但缺乏可识别性，削弱了其估计的因果有效性。为此，我们利用连续时间流模型建立多变量反事实识别基础，涵盖标准条件下的非马尔可夫情形。通过动态最优传输工具，刻画了流匹配生成唯一、单调且保持秩序的反事实传输映射的条件，确保推断一致性。在此基础上，我们在具有反事实真值的受控场景中验证理论，并在真实图像上提升了反事实合理性。
原文摘要 · Abstract (English)
We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.
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