[2510.08294] Counterfactual Identifiability via Dynamic Optimal Transport

Computer Science > Machine Learning arXiv:2510.08294 (cs) [Submitted on 9 Oct 2025 (v1), last revised 24 Mar 2026 (this version, v2)] Title:Counterfactual Identifiability via Dynamic Optimal Transport Authors:Fabio De Sousa Ribeiro, Ainkaran Santhirasekaram, Ben Glocker View a PDF of the paper titled Counterfactual Identifiability via Dynamic Optimal Transport, by Fabio De Sousa Ribeiro and 2 other authors View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG); Artificial Int...