Florian Gunsilius, Meng Hsuan Hsieh, Myung Jin Lee
arXiv 29 Jul 2022 · Statistics — Machine Learning
arXiv:2207.14727 · PDF · DOI · OpenAlex · Extracted main text
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and provides a unique solution in regular settings. The idea is to work on regular tangent cones of the Wasserstein space using generalized geodesics. Its structure and computational properties make the method applicable in a variety of settings, from causal inference to the analysis of object data. An application to estimating causal effects yields a generalization of the notion of synthetic controls to multivariate data with individual-level heterogeneity, as well as a way to estimate optimal weights jointly over all time periods.
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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 | Abadie, A. and Gardeazabal, J (2003) The economic costs of conflict: A case study of the basque country | 0.928 | 4 | 3 | 100% |
| 2 | Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program | 0.928 | 4 | 3 | 100% |
| 3 | Ambrosio, L., Gigli, N., and Savaré, G (2008) Gradient flows in metric spaces and in the space of probability measures | 0.819 | 20 | 3 | 55% |
| 4 | Bonneel, N., Peyré, G., and Cuturi, M (2016) Wasserstein barycentric coordinates: histogram regression using optimal transport | 0.811 | 4 | 2 | 100% |
| 5 | Villani, C (2003) Topics in optimal transportation | 0.737 | 3 | 3 | 67% |
| 6 | Zemel, Y. and Panaretos, V. M (2019) Fréchet means and procrustes analysis in wasserstein space | 0.737 | 3 | 3 | 67% |
| 7 | Abadie, A (2021) Using synthetic controls: Feasibility, data requirements, and methodological aspects | 0.737 | 3 | 2 | 100% |
| 8 | Gunsilius, F (2022) Distributional synthetic controls self | 0.737 | 3 | 2 | 100% |
| 9 | Peyré, G. and Cuturi, M (2019) Computational optimal transport | 0.737 | 3 | 2 | 100% |
| 10 | Agueh, M. and Carlier, G (2011) Barycenters in the Wasserstein Space | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 74 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Compositional Synthetic Controls | 0.405 | 1 | 1 |