Modelling gene expression dynamics with Gaussian process inference

Gaussian process (GP) inference provides a flexible nonparametric probabilistic modelling framework. We present examples of GP inference applied to time series gene expression data and for single-cell high-dimensional 'snapshot' expression data. We provide a brief overview of GP inference and show how GPs can be used to identify dynamic genes, infer degradation rates, model replicated and clustered time series, model stochastic single-cell dynamics, and model perturbations or branching in time series data. In the case of single-cell expression data we present a scalable implementation of the Gaussian process latent variable model, which can be used for dimensionality reduction and pseudo-time inference from single-cell RNA-sequencing data. We also present a recent approach to inference of branching dynamics in single-cell data. To scale up inference in these applications we use sparse variational Bayesian inference algorithms to deal with large matrix inversions and intractable likelihood functions.