Counterfactual Identifiability via Dynamic Optimal Transport

2025-10-09

AI Summary

This paper addresses the problem of counterfactual identification for high-dimensional multivariate outcomes. We propose a novel framework grounded in continuous-time flows and dynamic optimal transport (DOT), relaxing the conventional Markov and stationarity assumptions. Our method constructs an identifiable counterfactual mapping under non-Markovian and non-stationary regimes—marking the first integration of DOT into counterfactual reasoning. By coupling DOT with flow matching, we derive a unique, monotonic, and order-preserving transport map, thereby establishing theoretical guarantees for identifiability and consistency of causal estimands. The intervention path is modeled via continuous-time flows, and the framework is validated on controlled simulations and real image data, demonstrating adherence to axiomatic causal principles. Empirical results show substantial improvements in both theoretical rigor and practical effectiveness of counterfactual inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Identifies high-dimensional multivariate counterfactuals from observational data
• Establishes identifiability conditions using continuous-time flow matching
• Ensures unique monotone transport maps via dynamic optimal transport

Innovation

• Dynamic optimal transport enables counterfactual identifiability
• Continuous-time flows establish multivariate identification foundation
• Flow matching produces unique monotone transport maps