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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

Korean

Barycenter 단일 측정 가치 데이터에 대한 감독 및 감독되지 않은 학습에 유용한 것으로 나타났다.이 논문에서, 우리는 최근 제안된 Schrödinger-Bass Bridge (SBB) 사이의 최적 교통 브릿지에서 발생하는 데이터 스토하스틱 및 결정적인 최적 교통 브릿지를 사용합니다.이 모델의 각각에 대해, 우리의 첫 번째 이론적 결과는 grBB-barycenter underd mil assumptions의 존재를 입증합니다. 우리의 두 번째 이론적 결과는 Gaussians의 SBB-barycenter inter-symmetric의 디코더 문제를 특징으로합니다. 우리는 가우스 입력 최적화에 대한 이미지를 보여줍니다, 바라디아디아디아디아디아디아디아디아디아디아디아디아디아디아디아

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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