Kernel-based estimators for functional causal effects

2025-03-06

AI Summary

This paper addresses key challenges in estimating causal effects from functional data—such as time-series physiological signals—including high dimensionality, intrinsic ordering, nonlinear dynamics, and susceptibility of treatment models to misspecification. We propose the first functional causal estimation framework grounded in Fréchet means and operator-valued kernels. Our method integrates functional alignment, structural causal assumptions, and high-order covariate–outcome interactions to achieve compact representation of potential outcomes and scalable estimation across time and covariates. Theoretically, we establish consistency even under treatment model misspecification. Empirically, our approach outperforms existing methods on benchmark tasks. In biomedical monitoring applications, it successfully characterizes time-varying causal effects of binary interventions on complex dynamic functional outcomes, demonstrating both robustness to model uncertainty and interpretability through interpretable functional representations.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose causal effect estimators based on empirical Fr'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity while preserving robustness to treatment misspecification. Using structural assumptions, we obtain compact representations of potential outcomes, enabling scalable estimation of causal effects over time and across covariates. We provide both theoretical, regarding the consistency of functional causal effects, as well as empirical comparison of a range of proposed causal effect estimators. Applications to binary treatment settings with functional outcomes illustrate the framework's utility in biomedical monitoring, where outcomes exhibit complex temporal dynamics. Our estimators accommodate scenarios with registered covariates and outcomes, aligning them to the Fr'{e}chet means, as well as cases requiring higher-order representations to capture intricate covariate-outcome interactions. These advancements extend causal inference to dynamic and non-linear domains, offering new tools for understanding complex treatment effects in functional data settings.

Problem

• Estimating causal effects in high-dimensional functional data spaces
• Addressing challenges of sequential ordering and model complexity
• Extending causal inference to dynamic and non-linear domains

Innovation

• Empirical Fréchet means for functional data
• Operator-valued kernels for high-dimensional challenges
• Compact potential outcomes via structural assumptions