Trajectory Inference with Smooth Schrödinger Bridges

Wanli Hong, Yuliang Shi, Jonathan Niles-Weed
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:23722-23750, 2025.

Abstract

Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schrödinger Bridges. Our proposal generalizes prior work by allowing the reference process in the multi-marginal Schrödinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though naïvely smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Matérn processes) for which the resulting Smooth Schrödinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-hong25f, title = {Trajectory Inference with Smooth Schrödinger Bridges}, author = {Hong, Wanli and Shi, Yuliang and Niles-Weed, Jonathan}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {23722--23750}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/hong25f/hong25f.pdf}, url = {https://proceedings.mlr.press/v267/hong25f.html}, abstract = {Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schrödinger Bridges. Our proposal generalizes prior work by allowing the reference process in the multi-marginal Schrödinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though naïvely smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Matérn processes) for which the resulting Smooth Schrödinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets.} }
Endnote
%0 Conference Paper %T Trajectory Inference with Smooth Schrödinger Bridges %A Wanli Hong %A Yuliang Shi %A Jonathan Niles-Weed %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-hong25f %I PMLR %P 23722--23750 %U https://proceedings.mlr.press/v267/hong25f.html %V 267 %X Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schrödinger Bridges. Our proposal generalizes prior work by allowing the reference process in the multi-marginal Schrödinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though naïvely smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Matérn processes) for which the resulting Smooth Schrödinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets.
APA
Hong, W., Shi, Y. & Niles-Weed, J.. (2025). Trajectory Inference with Smooth Schrödinger Bridges. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:23722-23750 Available from https://proceedings.mlr.press/v267/hong25f.html.

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