Towards a mathematical theory of trajectory inference
Abstract
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time-point, and provide an efficient algorithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed globally over all time-points involving entropy-regularized optimal transport. We demonstrate that this problem can be solved efficiently in practice and yields good reconstructions, as we show on several synthetic and real datasets.
Keywords
Cite
@article{arxiv.2102.09204,
title = {Towards a mathematical theory of trajectory inference},
author = {Hugo Lavenant and Stephen Zhang and Young-Heon Kim and Geoffrey Schiebinger},
journal= {arXiv preprint arXiv:2102.09204},
year = {2023}
}
Comments
The first two authors contributed equally to this work; 76 pages