Counterfactual Identifiability via Dynamic Optimal Transport

• URL: http://arxiv.org/abs/2510.08294v1
• Date: Thu, 09 Oct 2025 14:45:13 GMT
• Title: Counterfactual Identifiability via Dynamic Optimal Transport
• Authors: Fabio De Sousa Ribeiro, Ainkaran Santhirasekaram, Ben Glocker,
• Abstract summary: We argue that counterfactuals must be identifiable to justify causal claims.<n>A recent line of work on counterfactual inference shows promising results but lacks identification.
• Score: 15.637845261800463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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