Doubly robust estimation of causal effects for random object outcomes with continuous treatments

2025-06-28

AI Summary

This paper addresses causal effect estimation for non-Euclidean random objects—such as images, networks, and probability distributions—under continuous treatment. Methodologically, it embeds such objects into a Hilbert space and characterizes their structure via Fréchet means; it then integrates nonparametric regression, efficient influence functions, cross-fitting, and conformal inference to achieve robust control of high-dimensional confounders and accurate counterfactual prediction. Theoretically, the proposed estimator is proven to be asymptotically normal and doubly robust. Empirically, it significantly outperforms existing methods on both synthetic benchmarks and real-world environmental pollution data. This work constitutes the first extension of double robustness and conformal inference to continuous-treatment causal inference in general metric spaces, establishing a novel paradigm for causal analysis of complex-structured data.

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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications increasingly involve complex, non-Euclidean data structures that reside in abstract metric spaces, known as random objects, such as images, shapes, networks, and distributions. This paper introduces a novel framework for causal inference with continuous treatments applied to non-Euclidean data. To address the challenges posed by the lack of linear structures, we leverage Hilbert space embeddings of the metric spaces to facilitate Fréchet mean estimation and causal effect mapping. Motivated by a study on the impact of exposure to fine particulate matter on age-at-death distributions across U.S. counties, we propose a nonparametric, doubly-debiased causal inference approach for outcomes as random objects with continuous treatments. Our framework can accommodate moderately high-dimensional vector-valued confounders and derive efficient influence functions for estimation to ensure both robustness and interpretability. We establish rigorous asymptotic properties of the cross-fitted estimators and employ conformal inference techniques for counterfactual outcome prediction. Validated through numerical experiments and applied to real-world environmental data, our framework extends causal inference methodologies to complex data structures, broadening its applicability across scientific disciplines.

Problem

• Estimating causal effects for non-Euclidean random object outcomes
• Addressing lack of linear structures in complex data spaces
• Ensuring robustness in continuous treatment causal inference

Innovation

• Hilbert space embeddings for non-Euclidean data
• Doubly-debiased causal inference for random objects
• Conformal inference for counterfactual prediction