We devise a theoretical framework and a numerical method to infer tra- jectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which pro- vide high dimensional measurements of cell states but cannot track the trajec- tories 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 algo- rithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed glob- ally 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.

Toward a mathematical theory of trajectory inference

Lavenant, Hugo;
2024

Abstract

We devise a theoretical framework and a numerical method to infer tra- jectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which pro- vide high dimensional measurements of cell states but cannot track the trajec- tories 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 algo- rithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed glob- ally 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.
2024
2024
Lavenant, Hugo; Zhang, Stephne; Kim, Young-Heon; Schiebinger, Geoffrey
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4063096
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