{"ID":2858211,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08294","arxiv_id":"2510.08294","title":"Counterfactual Identifiability via Dynamic Optimal Transport","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.","short_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 infere...","url_abs":"https://arxiv.org/abs/2510.08294","url_pdf":"https://arxiv.org/pdf/2510.08294v2","authors":"[\"Fabio De Sousa Ribeiro\",\"Ainkaran Santhirasekaram\",\"Ben Glocker\"]","published":"2025-10-09T14:45:13Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"stat.ML\"]","methods":"[]","has_code":false}