On the Mathematics of RNA Velocity II: Algorithmic Aspects (CSIAM Transactions on Applied Mathematics, 2024)
In the previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1–55], theauthors proposed a theoretical framework for the analysis of RNA velocity, whichis a promising concept in scRNA-seq data analysis to reveal the cell state-transitiondynamical processes underlying snapshot data. The current paper is devoted to thealgorithmic study of some key components in RNA velocity workflow. Four important points are addressed in this paper: (1) We construct a rational time-scale fixation method which can determine the global gene-shared latent time for cells. (2) Wepresent an uncertainty quantification strategy for the inferred parameters obtainedthrough the EM algorithm. (3) We establish the optimal criterion for the choice ofvelocity kernel bandwidth with respect to the sample size in the downstream analysisand discuss its implications. (4) We propose a temporal distance estimation approachbetween two cell clusters along the cellular development path. Some illustrative numerical tests are also carried out to verify our analysis. These results are intended toprovide tools and insights in further development of RNA velocity type methods inthe future.