Trajectory Inference with Smooth Schrödinger Bridges
Wanli Hong, Yuliang Shi, Jonathan Niles-Weed
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.
BibTeX
@inproceedings{
hong2025trajectory,
title={Trajectory Inference with Smooth Schr\"odinger Bridges},
author={Wanli Hong and Yuliang Shi and Jonathan Niles-Weed},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=GHyvvWu1XC}
}