用多边缘方法更准推断生物动态轨迹，还更快。
Multi-Marginal Schrödinger Bridge Matching
- 扩展迭代马尔可夫拟合，同时满足多个时间点分布约束
- 在真实单细胞数据上准确还原复杂演化路径，计算效率高
- 适合发育生物学、系统医学中无法追踪个体的轨迹推断
从离散时间快照理解种群的连续演化是关键挑战，尤其在发育生物学和系统医学中，个体纵向追踪常不可行。轨迹推断对揭示动态机制至关重要。虽然薛定谔桥（Schrödinger Bridge, SB）提供强大框架，但传统方法仅适用于两时间点，难以应对含多个中间快照的系统。本文提出多边缘薛定谔桥匹配（Multi-Marginal Schrödinger Bridge Matching, MSBM），一种专为多边缘SB问题设计的新算法。MSBM将迭代马尔可夫拟合（IMF）扩展至多边缘约束，有效确保所有中间边缘分布被严格遵守，同时保持全局动态的连续性。在合成数据与真实单细胞RNA测序数据上的实证表明，MSBM在捕捉复杂轨迹、尊重中间分布方面表现优异，且计算效率显著。
原文摘要 · Abstract (English)
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual entities is often impossible. Such trajectory inference is vital for unraveling the mechanisms of dynamic processes. While Schrödinger Bridge (SB) offer a potent framework, their traditional application to pairwise time points can be insufficient for systems defined by multiple intermediate snapshots. This paper introduces Multi-Marginal Schrödinger Bridge Matching (MSBM), a novel algorithm specifically designed for the multi-marginal SB problem. MSBM extends iterative Markovian fitting (IMF) to effectively handle multiple marginal constraints. This technique ensures robust enforcement of all intermediate marginals while preserving the continuity of the learned global dynamics across the entire trajectory. Empirical validations on synthetic data and real-world single-cell RNA sequencing datasets demonstrate the competitive or superior performance of MSBM in capturing complex trajectories and respecting intermediate distributions, all with notable computational efficiency.
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