Counterfactual Identifiability via Dynamic Optimal Transport
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912979600015360 |
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| author | Ribeiro, Fabio De Sousa Santhirasekaram, Ainkaran Glocker, Ben |
| author_facet | Ribeiro, Fabio De Sousa Santhirasekaram, Ainkaran Glocker, Ben |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counterfactual Identifiability via Dynamic Optimal Transport Ribeiro, Fabio De Sousa Santhirasekaram, Ainkaran Glocker, Ben Machine Learning Artificial Intelligence 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. |
| title | Counterfactual Identifiability via Dynamic Optimal Transport |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.08294 |