Satarupa Bhattacharjee, Bing Li, Xiao Wu, Lingzhou Xue
arXiv 28 Jun 2025 · Statistics — Methodology
arXiv:2506.22754 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kuchibhotla, Balakrishnan \ Wasserman (2023) `The hulc: confidence regions from convex hulls', J | 0.874 | 5 | 2 | 100% |
| 2 | Bhattacharjee, Li \ Xue (2025) `Nonlinear global Fréchet regression for random objects via weak conditional expectation', Ann | 0.843 | 3 | 3 | 100% |
| 3 | Petersen \ Müller (2019) `Fréchet regression for random objects with Euclidean predictors', Ann | 0.843 | 3 | 3 | 100% |
| 4 | Josey, Delaney, Wu, Nethery, DeSouza, Braun \ Dominici (2023) `Air pollution and mortality at the intersection of race and social class', New England Journal of Medicine 388(15), 1396–1404 | 0.811 | 4 | 2 | 100% |
| 5 | Billera, Holmes \ Vogtmann (2001) `Geometry of the space of phylogenetic trees', Advances in Applied Mathematics 27(4), 733–767 | 0.644 | 2 | 2 | 100% |
| 6 | Colangelo \ Lee (2025) `Double debiased machine learning nonparametric inference with continuous treatments', Journal of Business & Economic Statistics… | 0.644 | 2 | 2 | 100% |
| 7 | Fréchet (1948) `Les éléments aléatoires de nature quelconque dans un espace distancié', Annales de l'institut Henri Poincaré 10(4), 215–310 | 0.644 | 2 | 2 | 100% |
| 8 | Pearl, Glymour \ Jewell (2016) Causal Inference in Statistics: A Primer, Wiley | 0.644 | 2 | 2 | 100% |
| 9 | Rubin (2005) `Causal inference using potential outcomes: Design, modeling, decisions', J | 0.644 | 2 | 2 | 100% |
| 10 | Rubin (1974) `Estimating causal effects of treatments in randomized and nonrandomized studies.', Journal of Educational Psychology 66(5), 688 | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 59 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Random sets from the perspective of metric statistics | 0.405 | 1 | 1 |
| 2 | IV regression with distribution-valued outcomes | 0.405 | 1 | 1 |
| 3 | Wasserstein Policy Learning for Distributional Outcomes | 0.405 | 1 | 1 |
| 4 | A Test for Treatment Heterogeneity under a Distributional Difference-in-Difference Framework | 0.405 | 1 | 1 |