Inferring Unobserved Trajectories from Multiple Temporal Snapshots

June 23, 2026
Yunyi Shen & Carles Domingo-Enrich | Microsoft Research New England

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 Schrödinger 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 SBs). But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model family for the reference dynamic but not the exact values of the parameters within it. So I propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a family of reference dynamics, not a single fixed one. I demonstrate the advantages of my method on simulated and real data, across applications in biology and oceanography.

Speaker bio: Yunyi Shen recently got his Ph.D. from the Department of Electrical Engineering and Computer Science at MIT. He works in probabilistic machine learning and statistics on problems where data are scarce or noisy, and as a result require adaptive data collection, incorporation of domain-specific structure, and careful downstream evaluation. Drawing on a background in the physical and life sciences, his work is shaped by close interdisciplinary collaborations and motivated by scientific problems in biology and physics, such as gene regulation, fluid dynamics in cells, wildlife monitoring, and time-domain astronomy.

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