提出函数空间KL散度估算方法，解决轨迹推断的评估难题。
Relative Entropy Estimation in Function Space: Theory and Applications to Trajectory Inference
- 基于函数空间概率测度的KL散度估计，可数据驱动计算。
- 在合成与真实单细胞数据上验证，估算值接近理论值。
- 揭示现有评估指标不一致问题，适合稀疏数据场景评估。
轨迹推断（TI）旨在从快照数据中恢复潜在动态过程，其中仅可观测到时间索引边缘分布的独立样本。在单细胞基因组学等应用中，破坏性测量导致路径空间分布无法从有限边缘分布中唯一识别，使留出边缘预测成为主流但受限的评估方式。本文提出一种通用框架，用于估计函数空间上概率测度之间的Kullback-Leibler（KL）散度，得到一个可扩展、数据驱动的估计器，适用于真实快照数据集。我们在基准测试中验证了估计器的准确性，发现估算的函数空间KL与解析解高度吻合。将该框架应用于合成与真实scRNA-seq数据集，结果显示当前评估指标常给出矛盾结论，而路径空间KL能实现轨迹推断方法的连贯比较，并暴露推断动力学在数据稀疏或缺失区域的差异。这些结果支持函数空间KL作为部分可观测条件下轨迹推断的合理评估准则。
原文摘要 · Abstract (English)
Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make path-space laws non-identifiable from finitely many marginals, leaving held-out marginal prediction as the dominant but limited evaluation protocol. We introduce a general framework for estimating the Kullback-Leibler divergence (KL) divergence between probability measures on function space, yielding a tractable, data-driven estimator that is scalable to realistic snapshot datasets. We validate the accuracy of our estimator on a benchmark suite, where the estimated functional KL closely matches the analytic KL. Applying this framework to synthetic and real scRNA-seq datasets, we show that current evaluation metrics often give inconsistent assessments, whereas path-space KL enables a coherent comparison of trajectory inference methods and exposes discrepancies in inferred dynamics, especially in regions with sparse or missing data. These results support functional KL as a principled criterion for evaluating trajectory inference under partial observability.
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