Causal Inference with Cocycles

2024-05-22

AI Summary

Identifying counterfactual joint distributions (i.e., couplings) is essential for personalized decision-making and risk assessment, yet existing approaches—bijective structural causal models (SCMs) and optimal transport (OT)—suffer from sensitivity to noise misspecification and inability to identify higher-order couplings, respectively. This paper introduces a novel framework grounded in *cocycles*—a concept from dynamical systems theory newly imported into causal inference—to characterize invariant structures via local symmetries under intervention-induced transformations. Our approach enables nonparametric, model-free identification of counterfactual distributions without relying on parametric or semiparametric assumptions. Crucially, it is inherently robust to latent variable misspecification. We develop an efficient semiparametric cocycle estimator, demonstrating both robustness and state-of-the-art performance in simulations. Applied to 401(k) policy evaluation, our method accurately quantifies the causal effect of pension eligibility on household asset accumulation.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Many interventions in causal inference can be represented as transformations. We identify a local symmetry property satisfied by a large class of causal models under such interventions. Where present, this symmetry can be characterized by a type of map called a cocycle, an object that is central to dynamical systems theory. We show that such cocycles exist under general conditions and are sufficient to identify interventional and counterfactual distributions. We use these results to derive cocycle-based estimators for causal estimands and show they achieve semiparametric efficiency under typical conditions. Since (infinitely) many distributions can share the same cocycle, these estimators make causal inference robust to mis-specification by sidestepping superfluous modelling assumptions. We demonstrate both robustness and state-of-the-art performance in several simulations, and apply our method to estimate the effects of 401(k) pension plan eligibility on asset accumulation using a real dataset.

Problem

• Estimating joint distributions for counterfactual outcomes
• Bridging structural models and optimal transport methods
• Providing coherent counterfactual transports with identifiability guarantees

Innovation

• Counterfactual cocycles bridge SCM and OT gaps
• Cocycles provide coherence and identifiability guarantees
• Invariant to latent noise distribution avoiding mis-specification