136 research outputs found
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
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
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
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
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