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Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data

Ngoc-Hai Nguyen, Thuan Nguyen, Prakash Ishwar, Shuchin Aeron · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29227 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

在这篇论文中,我们使用在最近提出的Schrödinger-Bass桥(SBB)两种测量尺寸之间产生的数据斯托加斯蒂克和确定性的最佳运输桥梁,对(概率)测量估值数据的监督和无监督学习有用,并提出SBB-encoder,Marbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarbarb

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Interpolation (computer graphics), Measure (data warehouse), Context (archaeology), Gradient descent, Algorithm, Computer science

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