Methods for reconstructing developmental trajectories from time series single cell RNA-Seq (scRNA-Seq) data can be largely divided into two categories. The first, often referred to as psuedotime ordering methods, are deterministic relying on dimensionality reduction followed by an ordering step. The second learns a probabilistic branching model to represent the underlying developmental process being studied. While both types of methods have been successfully applied, each suffers from shortcomings that limit their general applicability. To address these issues we developed a new method based on continuous state HMMs (CSHMMs) for representing and modeling time series scRNA-Seq data. We define the CSHMM model and provide efficient learning and inference algorithms which allow the method to determine both the structure of the branching process and the assignment of cells to these branches. Analyzing two developmental single cell datasets we show that the CSHMM method accurately infers the branching topology and that it is able to correctly and continuously assign cells to paths, in both cases improving upon prior methods proposed for this task. Analysis of genes based on the continuous cell assignment identifies known and novel markers for several different cell types.
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