# Statistical learning in Wasserstein space

arXiv: https://arxiv.org/abs/2004.07875 · HTML: https://mlsanity.com/paper/2004.07875/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [On the complexity of the optimal transport problem with graph-structured cost](https://mlsanity.com/paper/2110.00627/) (2021)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)

## Abstract (arXiv)

We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation allows efficient computation, ensures existence of optimal solutions, and admits a probabilistic interpretation over the space of paths (line segments). Application of the theory to the interpolation of empirical distributions, images, power spectra, as well as assessing uncertainty in experimental designs, is envisioned.