TOWARD A MATHEMATICAL THEORY OF TRAJECTORY INFERENCE

• 成果类型: Article
• 署名作者: Lavenant, Hugo; Zhang, Stephen; Kim, Young-Heon; Schiebinger, Geoffrey
• 署名单位: Bocconi University; Bocconi University; University of British Columbia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1969
• 发表日期: 2024
• 页码: 428-500
• 关键词: genome-wide expression; Optimal Transport; minimization; RESOLUTION; DYNAMICS; equation; distance; time

摘要

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 data sets.