Joint Structure Learning of Multiple Non-Exchangeable Networks

Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to have similar structures. However, in many practical applications, exchangeability in this sense may not hold, as some pairs of networks may be more closely related than others, for example due to group and sub-group structure in the data. Here we present a novel Bayesian formulation that generalises joint structure learning beyond the exchangeable case. In addition to a general framework for joint learning, we (i) provide a novel default prior over the joint structure space that requires no user input; (ii) allow for latent networks; (iii) give an efficient, exact algorithm for the case of time series data and dynamic Bayesian networks. We present empirical results on non-exchangeable populations, including a real data example from biology, where cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS

Towards a Multi-Subject Analysis of Neural Connectivity

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances it is natural to leverage similarity between subjects to improve statistical efficiency. The first exact algorithm for estimation of multiple related DAGs was recently proposed by Oates et al. 2014; in this letter we present examples and discuss implications of the methodology as applied to the analysis of fMRI data from a multi-subject experiment. Elicitation of tuning parameters requires care and we illustrate how this may proceed retrospectively based on technical replicate data. In addition to joint learning of subject-specific connectivity, we allow for heterogeneous collections of subjects and simultaneously estimate relationships between the subjects themselves. This letter aims to highlight the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2

Bayesian inference for protein signalling networks

Cellular response to a changing chemical environment is mediated by a complex system of interactions involving molecules such as genes, proteins and metabolites. In particular, genetic and epigenetic variation ensure that cellular response is often highly specific to individual cell types, or to different patients in the clinical setting. Conceptually, cellular systems may be characterised as networks of interacting components together with biochemical parameters specifying rates of reaction. Taken together, the network and parameters form a predictive model of cellular dynamics which may be used to simulate the effect of hypothetical drug regimens. In practice, however, both network topology and reaction rates remain partially or entirely unknown, depending on individual genetic variation and environmental conditions. Prediction under parameter uncertainty is a classical statistical problem. Yet, doubly uncertain prediction, where both parameters and the underlying network topology are unknown, leads to highly non-trivial probability distributions which currently require gross simplifying assumptions to analyse. Recent advances in molecular assay technology now permit high-throughput data-driven studies of cellular dynamics. This thesis sought to develop novel statistical methods in this context, focussing primarily on the problems of (i) elucidating biochemical network topology from assay data and (ii) prediction of dynamical response to therapy when both network and parameters are uncertain

A Riemannian-Stein Kernel Method

This paper presents a theoretical analysis of numerical integration based on interpolation with a Stein kernel. In particular, the case of integrals with respect to a posterior distribution supported on a general Riemannian manifold is considered and the asymptotic convergence of the estimator in this context is established. Our results are considerably stronger than those previously reported, in that the optimal rate of convergence is established under a basic Sobolev-type assumption on the integrand. The theoretical results are empirically verified on $\mathbb{S}^2$