Modelling Sequential Branching Dynamics with a Multivariate Branching Gaussian Process

Abstract

The Branching Gaussian Process (BGP) model is a modification of the Overlapping Mixture of Gaussian Processes (OMGP) where latent functions branch in time. The BGP model was introduced as a method to model bifurcations in single-cell gene expression data and order genes by inferring their branching time parameter. A limitation of the current BGP model is that the assignment of observations to latent functions is inferred independently for each output dimension (gene). This leads to inconsistent assignments across outputs and reduces the accuracy of branching time inference. Here, we propose a multivariate branching Gaussian process (MBGP) model to perform joint branch assignment inference across multiple output dimensions. This ensures that branch assignments are consistent and leverages more data for branching time inference. Model inference is more challenging than for the original BGP or OMGP models because assignment labels can switch from trunk to branch lineages as branching times change during inference. To scale up inference to large datasets we use sparse variational Bayesian inference. We examine the effectiveness of our approach on synthetic data and a single-cell RNA-Seq dataset from mouse haematopoietic stem cells (HSCs). Our approach ensures assignment consistency by design and achieves improved accuracy in branching time inference and assignment accuracy.