糖心TV

Gaussian processes provide a convenient and flexible class of non-parametric model for temporal and spatial data. We are applying Gaussian processes in a range of biological applications involving high-throughput time course data, e.g. modelling the elongation dynamics of polymerase, uncovering mRNA production delays, inferring regulatory networks and most recently identifying perturbations and bifurcations from high-throughput expression data. I will provide an overview of Gaussian process inference and describe some of our recent work in modelling gene expression dynamics. Most recently we have been focusing on single-cell data. Using longitudinal data from microscopy experiments we are using stochastic periodic processes to uncover periodicity controlled by negative feedback loops. Using genome-wide single-cell expression data we are uncovering branching processes and uncovering the order with which different genes differentiate through a developmental process.

We make two contributions to Bayesian machine learning algorithms.

Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions.

Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates.

Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a dataset is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Markov chain Monte Carlo (MCMC) sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster.

This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks.