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

arXiv: https://arxiv.org/abs/2506.22754 · HTML: https://mlsanity.com/paper/2506.22754/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Causal inference methods for combining randomized trials and observational studies: a review](https://mlsanity.com/paper/2011.08047/) (2020)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels](https://mlsanity.com/paper/1412.0265/) (2014)
- [Causal Inference on Distribution Functions](https://mlsanity.com/paper/2101.01599/) (2021)
- [Uniform convergence of local Fr'echet regression, with applications to locating extrema and time warping for metric space valued trajectories](https://mlsanity.com/paper/2006.13548/) (2020)
- [Nonlinear global Fr'echet regression for random objects via weak conditional expectation](https://mlsanity.com/paper/2310.07817/) (2023)
- [Matching on Generalized Propensity Scores with Continuous Exposures](https://mlsanity.com/paper/1812.06575/) (2018)
- [Geodesic Causal Inference](https://mlsanity.com/paper/2406.19604/) (2024)
- [The HulC: Confidence Regions from Convex Hulls](https://mlsanity.com/paper/2105.14577/) (2021)
- [Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces](https://mlsanity.com/paper/2405.13970/) (2024)
- [Collaborative Representation for SPD Matrices with Application to Image-Set Classification](https://mlsanity.com/paper/2201.08962/) (2022)

## Built on by (most cited first, 5 of 5)

- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability](https://mlsanity.com/paper/2603.14169/) (2026)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)
- [Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects](https://mlsanity.com/paper/2607.28981/) (2026)
- [Causal inference for group-contaminated structured outcomes: observable quotients, lossless reduction and exact randomization inference](https://mlsanity.com/paper/2608.11954/) (2026)

## Abstract (arXiv)

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 Fr'echet 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.