# Generalized Wasserstein Barycenters

arXiv: https://arxiv.org/abs/2411.06838 · HTML: https://mlsanity.com/paper/2411.06838/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)

## Abstract (arXiv)

We study the existence and uniqueness of the barycenter of a signed distribution of probability measures on a Hilbert space. The barycenter is found, as usual, as a minimum of a functional. In the case where the positive part of the signed measure is atomic, we can show also uniqueness. In the one-dimensional case, we characterize the quantile function of the unique minimum as the orthogonal projection of the L2-barycenter of the quantiles on the cone of nonincreasing functions in L2(0,1). Further, we provide a stability estimate in dimension one and a counterexample to uniqueness in ℝ2. Finally, we address the consistency of the barycenters and we prove that barycenters of a sequence of approximating measures converge (up to subsequences) to a barycenter of the limit measure.