arXiv 8 Dec 2021 · Statistics — Methodology · 3 citations (OpenAlex)
arXiv:2112.04398 · PDF · DOI · OpenAlex · Extracted main text
Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to address this, with different advantages and drawbacks in computational and statistical performance as well as interpretability. This article introduces a natural optimal matching method based on multimarginal unbalanced optimal transport that possesses many useful properties in this regard. It provides interpretable weights based on the distance of matched individuals, can be efficiently implemented via the iterative proportional fitting procedure, and can match several treatment arms simultaneously. Importantly, the proposed method only selects good matches from either group, hence is competitive with the classical k-nearest neighbors approach in terms of bias and variance in finite samples. Moreover, we prove a central limit theorem for the empirical process of the potential functions of the optimal coupling in the unbalanced optimal transport problem with a fixed penalty term. This implies a parametric rate of convergence of the empirically obtained weights to the optimal weights in the population for a fixed penalty term.
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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 | Harchaoui, Liu \ Pal (2020) `Asymptotics of entropy-regularized optimal transport via chaos decomposition', arXiv preprint 2011.08963 | 1.000 | 6 | 3 | 100% |
| 2 | Séjourné, Feydy, Vialard, Trouvé \ Peyré (2019) `Sinkhorn divergences for unbalanced optimal transport', arXiv preprint:1910.12958 | 0.879 | 25 | 5 | 68% |
| 3 | Abadie \ Imbens (2006) `Large sample properties of matching estimators for average treatment effects', Econometrica 74(1), 235–267 | 0.874 | 5 | 2 | 100% |
| 4 | Imbens (2000) `The role of the propensity score in estimating dose-response functions', Biometrika 87(3), 706–710 | 0.874 | 5 | 2 | 100% |
| 5 | Peyré \ Cuturi (2019) `Computational optimal transport', Foundations and Trends in Machine Learning 11(5-6), 355–607 | 0.811 | 4 | 2 | 100% |
| 6 | Abadie, Drukker, Herr \ Imbens (2004) `Implementing matching estimators for average treatment effects in STATA', The STATA journal 4(3), 290–311 | 0.737 | 3 | 2 | 100% |
| 7 | Carlier (2021) On the linear convergence of the multi-marginal Sinkhorn algorithm | 0.737 | 3 | 2 | 100% |
| 8 | Chizat, Peyré, Schmitzer \ Vialard (2018) `Scaling algorithms for unbalanced optimal transport problems', Mathematics of Computation 87(314), 2563–2609 | 0.737 | 3 | 2 | 100% |
| 9 | di Marino \ Gerolin (2020) `An optimal transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm', Journal of Scientific… | 0.737 | 3 | 2 | 100% |
| 10 | Stuart (2010) `Matching methods for causal inference: A review and a look forward', Statistical Science 25(1), 1 | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 84 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | An econometrician's guide to optimal transport | 0.585 | 3 | 1 |
| 2 | Estimating Functionals of the Joint Distribution of Potential Outcomes with Optimal Transport | 0.405 | 1 | 1 |
| 3 | Inference in partially identified moment models via regularized optimal transport | 0.405 | 1 | 1 |