Active Timepoint Selection for Learning Measure-Valued Trajectories

2026-05-28

AI Summary

This work addresses the challenge of reconstructing continuous probability distribution trajectories and optimizing sampling time points from sparse, destructive, and costly snapshot data, as commonly encountered in single-cell biology. It introduces active learning into measure-valued trajectory modeling in Wasserstein space for the first time. By leveraging Linearized Optimal Transport (LOT), distributional snapshots are embedded into a tangent space, where a Gaussian process surrogate model is constructed to quantify epistemic uncertainty. The method iteratively selects the most informative time points for measurement based on this uncertainty-aware model. Experiments demonstrate that the proposed approach significantly outperforms baselines that ignore uncertainty, achieving markedly improved reconstruction accuracy of probabilistic trajectories under sparse observational settings, both on synthetic and real-world data.

Abstract

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Problem

• active learning
• measure-valued trajectories
• Wasserstein space
• epistemic uncertainty
• timepoint selection

Innovation

• active learning
• measure-valued trajectories
• Linearized Optimal Transport
• Gaussian Process
• Wasserstein space