Multi-marginal Schrödinger Bridges with Iterative Reference Refinement

Yunyi Shen, Renato Berlinghieri, Tamara Broderick
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3817-3825, 2025.

Abstract

Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g. given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell’s life cycle. But sequencing any cell destroys that cell. So we can access data for any particular cell only at a single time point, but we have data across many cells. The deep learning community has recently explored using Schr{ö}dinger bridges (SBs) and their extensions in similar settings. However, existing methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic (often set to Brownian motion within SB). But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. We demonstrate the advantages of our method on simulated and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-shen25b, title = {Multi-marginal Schr{ö}dinger Bridges with Iterative Reference Refinement}, author = {Shen, Yunyi and Berlinghieri, Renato and Broderick, Tamara}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3817--3825}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/shen25b/shen25b.pdf}, url = {https://proceedings.mlr.press/v258/shen25b.html}, abstract = {Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g. given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell’s life cycle. But sequencing any cell destroys that cell. So we can access data for any particular cell only at a single time point, but we have data across many cells. The deep learning community has recently explored using Schr{ö}dinger bridges (SBs) and their extensions in similar settings. However, existing methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic (often set to Brownian motion within SB). But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. We demonstrate the advantages of our method on simulated and real data.} }
Endnote
%0 Conference Paper %T Multi-marginal Schrödinger Bridges with Iterative Reference Refinement %A Yunyi Shen %A Renato Berlinghieri %A Tamara Broderick %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-shen25b %I PMLR %P 3817--3825 %U https://proceedings.mlr.press/v258/shen25b.html %V 258 %X Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g. given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell’s life cycle. But sequencing any cell destroys that cell. So we can access data for any particular cell only at a single time point, but we have data across many cells. The deep learning community has recently explored using Schr{ö}dinger bridges (SBs) and their extensions in similar settings. However, existing methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic (often set to Brownian motion within SB). But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. We demonstrate the advantages of our method on simulated and real data.
APA
Shen, Y., Berlinghieri, R. & Broderick, T.. (2025). Multi-marginal Schrödinger Bridges with Iterative Reference Refinement. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3817-3825 Available from https://proceedings.mlr.press/v258/shen25b.html.

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