论文标题
路径空间中通过平均场兰格文的轨迹推断
Trajectory Inference via Mean-field Langevin in Path Space
论文作者
论文摘要
轨迹推断旨在从其时间边缘的快照中恢复人群的动态。为了解决这项任务，Lavenant等人引入了相对于路径空间中的Wiener度量的最小渗透估计量。 ARXIV：2102.09204，并显示出从无限尺寸凸优化问题的解决方案中始终如一地恢复大量漂移扩散过程的动力学。在本文中，我们引入了一种无网算法来计算该估计器。我们的方法包括通过schrödinger桥的一个点云（每个快照）的家族，该桥随着嘈杂的梯度下降而演变。我们研究动力学的平均场极限，并证明其全球收敛到所需的估计器。总体而言，这导致了一种具有端到端理论保证的推理方法，可以解决轨迹推理的可解释模型。我们还提出了如何调整方法处理质量变化的方法，这是处理单个细胞RNA序列数据时细胞可以分支并死亡的有用扩展。
Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener measure in path space was introduced by Lavenant et al. arXiv:2102.09204, and shown to consistently recover the dynamics of a large class of drift-diffusion processes from the solution of an infinite dimensional convex optimization problem. In this paper, we introduce a grid-free algorithm to compute this estimator. Our method consists in a family of point clouds (one per snapshot) coupled via Schrödinger bridges which evolve with noisy gradient descent. We study the mean-field limit of the dynamics and prove its global convergence to the desired estimator. Overall, this leads to an inference method with end-to-end theoretical guarantees that solves an interpretable model for trajectory inference. We also present how to adapt the method to deal with mass variations, a useful extension when dealing with single cell RNA-sequencing data where cells can branch and die.
