TY - JOUR
T1 - On the Mathematics of RNA Velocity II: Algorithmic Aspects
AU - Li , Tiejun
AU - Wang , Yizhuo
AU - Yang , Guoguo
AU - Zhou , Peijie
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 182
EP - 220
PY - 2024
DA - 2024/02
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2023-0026
UR - https://global-sci.org/intro/article_detail/csiam-am/22924.html
KW - Time-scale fixation, uncertainty quantification, optimal kernel bandwidth, temporal distance estimation.
AB - <p style="text-align: justify;">In the previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1–55], the
authors proposed a theoretical framework for the analysis of RNA velocity, which
is a promising concept in scRNA-seq data analysis to reveal the cell state-transition
dynamical processes underlying snapshot data. The current paper is devoted to the
algorithmic 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) We
present an uncertainty quantification strategy for the inferred parameters obtained
through the EM algorithm. (3) We establish the optimal criterion for the choice of
velocity kernel bandwidth with respect to the sample size in the downstream analysis
and discuss its implications. (4) We propose a temporal distance estimation approach
between two cell clusters along the cellular development path. Some illustrative numerical tests are also carried out to verify our analysis. These results are intended to
provide tools and insights in further development of RNA velocity type methods in
the future.</p>