主动选择测量时间，精准重建概率轨迹变化过程。
Active Timepoint Selection for Learning Measure-Valued Trajectories
- 用线性最优传输将分布映射到切空间，构建高斯过程代理模型
- 在真实与合成数据上显著降低不确定性，优于无不确定性感知基线
- 适合单细胞生物学等需稀疏采样的动态概率建模场景
从稀疏快照推断连续概率路径是单细胞生物学等领域的基础挑战，因高保真数据获取常具破坏性且测序成本高昂。这催生了主动学习策略以智能选择最优测量时间。然而，该任务仍属开放问题：目标对象位于无限维 Wasserstein 空间，标准欧氏度量不适用，现有插值方法缺乏认知不确定性量化。本文提出一个将主动实验扩展至测度空间的框架。通过线性最优传输（LOT），将分布快照映射至切空间，使其适用于高斯过程建模，从而构建底层概率路径的可处理概率代理模型。由此生成的采集策略可迭代选择最小化不确定性的测量时间。实验表明，该方法在合成与真实数据集上均显著优于无不确定性感知基线。
原文摘要 · Abstract (English)
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.
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