Gaussian processes provide flexible non-parametric models of data and we are using them to model temporal and spatial patterns in gene expression. Single-cell omics measurements are destructive and one cannot follow the high-dimensional dynamics of genes across time in one cell. Similarly, the spatial context of cells is often lost or only known with reduced resolution. Computational methods are widely used to infer pseudo-temporal orderings of cells or to infer spatial locations. We show how Gaussian processes (GPs) can be used to model temporal and spatial relationships between genes and cells in these datasets. As examples I will show how we use Bayesian GPLVMs with informative priors to infer pseudo-temporal orderings for single-cell time course data  and branching GPs to identify gene-specific bifurcation points across pseudotime . Gene expression data are often summarized as counts and there may be many zero values in the data due to limited sequencing depth. We therefore recently extended these methods to use negative binomial or zero-inflated negative binomial likelihoods and we show that this can lead to much improved performance over standard Gaussian noise models when identifying spatially varying genes from spatial transcriptomics data .
 Ahmed, S., Rattray, M., & Boukouvalas, A. (2019). GrandPrix: scaling up the Bayesian GPLVM for single-cell data. Bioinformatics, 35(1), 47-54.
 Boukouvalas, A., Hensman, J., & Rattray, M. (2018). BGP: identifying gene-specific branching dynamics from single-cell data with a branching Gaussian process. Genome biology, 19(1), 65.
 BinTayyash, N., Georgaka, S., John, S. T., Ahmed, S., Boukouvalas, A., Hensman, J., & Rattray, M. (2020). Non-parametric modelling of temporal and spatial counts data from RNA-seq experiments. Bioarxiv https://doi.org/10.1101/2020.07.29.227207
Magnus Rattray is Professor of Computational and Systems Biology at the University of Manchester and Director of the Institute for Data Science & AI. He works on the development of methods for machine learning and Bayesian inference with applications to large-scale biological and medical datasets. He has a long-standing interest in longitudinal data analysis and a more recent interest in modelling single-cell, spatial omics and live cell imaging microscopy data. He is a Fellow of the ELLIS Health Programme and the Alan Turing Institute and his research is funded by a Wellcome Trust Investigator Award.