e-Article
Toward a mathematical theory of trajectory inference.
Document Type
Journal
Author
Lavenant, Hugo (I-UCOM-DTA) AMS Author Profile; Zhang, Stephen (3-BC) AMS Author Profile; Kim, Young-Heon (3-BC) AMS Author Profile; Schiebinger, Geoffrey (3-BC) AMS Author Profile
Source
Subject
49 Calculus of variations and optimal control; optimization -- 49M Numerical methods
49M29Methods involving duality
62Statistics -- 62G Nonparametric inference
62G99None of the above, but in this section
92Biology and other natural sciences -- 92C Physiological, cellular and medical topics
92C15Developmental biology, pattern formation
49M29
62
62G99
92
92C15
Language
English
Abstract
Summary: ``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.''