Tightening Causal Bounds via Covariate-Aware Optimal Transport

2025-02-03

AI Summary

In causal inference, partial identification (PI) intervals often suffer from excessive width due to outcome distribution heterogeneity between treatment and control groups, undermining their decision-making utility. To address this, we propose Covariate-aware Optimal Transport Relaxation (COT-R), the first method to reformulate the conditional optimal transport problem as a standard optimal transport problem—thereby preserving covariate adjustment capability while ensuring computational tractability. Leveraging Lagrangian duality and penalty methods, COT-R constructs asymptotically sharp, uniformly tighter relaxation bounds that dominate the original conditional optimal transport bounds for all regularization parameters. We establish theoretical guarantees showing that the estimator achieves the minimax optimal convergence rate. Extensive simulations demonstrate an average 37% reduction in PI width, outperforming existing covariate-weighting and distributionally robust approaches. Moreover, COT-R is compatible with mainstream optimal transport solvers (e.g., POT, GeomLoss).

Technology Category

• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Causal Learning

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.

Problem

• Narrowing causal bounds using covariate-aware optimal transport
• Reducing partial identification intervals via covariate adjustment
• Simplifying conditional optimal transport to standard optimal transport

Innovation

• Reduces conditional optimal transport to standard OT
• Incorporates covariates for narrower identification intervals
• Data-driven estimator using existing OT packages