用平滑高斯过程改进轨迹推断，生成更自然的细胞演化路径。
Trajectory Inference with Smooth Schrödinger Bridges
- 将参考过程设为光滑高斯过程，提升轨迹连续性
- 针对马特恩过程等可解类，实现多项式时间求解
- 在真实和模拟单细胞数据上优于现有方法
为应对轨迹推断与粒子追踪的应用需求，我们提出平滑薛定谔桥（Smooth Schrödinger Bridges）。该方法将薛定谔桥问题中的参考过程推广为平滑高斯过程，从而在应用中生成更规则、可解释的轨迹。尽管直接平滑参考过程会导致计算不可行，但我们识别出一类可解过程（包括马特恩过程），其对应的平滑薛定谔桥问题可被映射到相空间上的简化问题，并可在多项式时间内求解。我们开发了一种实用近似算法，在多个模拟及真实单细胞RNAseq数据集上表现优于现有方法。代码已开源：https://github.com/WanliHongC/Smooth_SB。
原文摘要 · Abstract (English)
Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schrödinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schrödinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though naïvely smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Matérn processes) for which the resulting Smooth Schrödinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. The code can be found at https://github.com/WanliHongC/Smooth_SB
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