Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data
Abstract
Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual drift-diffusion control arising in the recently proposed Schrödinger-Bass Bridge (SBB) between two measures, and propose \textit{SBB-encoder}, \textit{SBB-decoder}, \textit{SBB-symmetric}, and \textit{SBB-Markovian} barycenter models. For each of these novel models, our first theoretical result establishes the existence of the SBB-barycenter under mild assumptions. Our second theoretical result characterizes the decoder SBB-barycenter of Gaussians where we show that for Gaussian input measures, the decoder formulation admits a Gaussian minimizer, reducing barycenter computation to a finite-dimensional optimization and yielding a compact algorithm. For general input measures, we derive a hybrid Wasserstein gradient particle descent scheme for all four formulations using the SBB dual representation. Finally, we utilize these algorithms for solving distributional-inverse/interpolation problems arising in the context of spatial images and single-cell RNA sequencing data, where we show that the SBB-decoder and Markovian barycenter allow us to interpolate between successive time points. Results show that our method outperforms existing barycenter models for measure interpolation and inference.
Related
- Exponential Convergence of the Sinkhorn Algorithm for the Schrödinger Bridge with Regime Switching
- Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight
- From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit
- Balance laws with measure valued source for commuting dynamics
- Semilinear Neumann boundary value problems for measure-valued maps
BibTeX
@misc{nguyen2026schrödingerbass,
title = {{Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data}},
author = {Ngoc-Hai Nguyen and Thuan Nguyen and Prakash Ishwar and Shuchin Aeron},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29227},
eprint = {2610.29227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29227},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data
AU - Ngoc-Hai Nguyen
AU - Thuan Nguyen
AU - Prakash Ishwar
AU - Shuchin Aeron
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29227
UR - https://arxiv.org/abs/2610.29227
AB - Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual drift-diffusion control arising in the recently proposed Schrödinger-Bass Bridge (SBB) between two measures, and propose \textit{SBB-encoder}, \textit{SBB-decoder}, \textit{SBB-symmetric}, and \textit{SBB-Markovian} barycenter models. For each of these novel models, our first theoretical result establishes the existence of the SBB-barycenter under mild assumptions. Our second theoretical result characterizes the decoder SBB-barycenter of Gaussians where we show that for Gaussian input measures, the decoder formulation admits a Gaussian minimizer, reducing barycenter computation to a finite-dimensional optimization and yielding a compact algorithm. For general input measures, we derive a hybrid Wasserstein gradient particle descent scheme for all four formulations using the SBB dual representation. Finally, we utilize these algorithms for solving distributional-inverse/interpolation problems arising in the context of spatial images and single-cell RNA sequencing data, where we show that the SBB-decoder and Markovian barycenter allow us to interpolate between successive time points. Results show that our method outperforms existing barycenter models for measure interpolation and inference.
ER -