mlsanityData to 7 Oct 2026

Tangential Wasserstein Projections

arXiv 2207.14727 ↗First posted 29 Jul 2022stat.ML cs.LG econ.EMcited by 4

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 26 of its 95 references that are in the map. First posted on arXiv 29 Jul 2022.

Builds on

26 of 95 references.

References · 26

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2018BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learningcited by 1,282
  3. 2018Computational Optimal Transportcited by 765
  4. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
  5. 2019Optimal transport mapping via input convex neural networkscited by 202
  6. 2017A Rewriting System for Convex Optimization Problemscited by 178
  7. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  8. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 95
  9. 2021Entropic estimation of optimal transport mapscited by 87
  10. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  11. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  12. 2018Statistical Optimal Transport via Factored Couplingscited by 38
14 more
  1. 2020Wasserstein Regressioncited by 35
  2. 2019On Robustness of Principal Component Regressioncited by 27
  3. 2019Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein spacecited by 25
  4. 2015Discrete Wasserstein Barycenters: Optimal Transport for Discrete Datacited by 20
  5. 2017Fr'echet Means and Procrustes Analysis in Wasserstein Spacecited by 18
  6. 2019A fast approach to optimal transport: The back-and-forth methodcited by 16
  7. 2021Distribution-on-Distribution Regression via Optimal Transport Mapscited by 16
  8. 2020Distributional synthetic controlscited by 9
  9. 2022Measure Estimation in the Barycentric Coding Modelcited by 9
  10. 2017Log-PCA versus Geodesic PCA of histograms in the Wasserstein spacecited by 5
  11. 2021A Design-Based Perspective on Synthetic Control Methodscited by 5
  12. 2021A novel notion of barycenter for probability distributions based on optimal weak mass transportcited by 5
  13. 2022Synthetic Control As Online Linear Regressioncited by 5
  14. 2013Geodesic PCA in the Wasserstein spacecited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 0; 2026: 2.

4 papers.

  1. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  2. 2024Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applicationscited by 1
  3. 2026Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphscited by 0
  4. 2026Conditional Random Ordered Transport Spacescited by 0