arXiv subjects

Alun Thomas

Publications and source records attributed to Alun Thomas.

4 recordsLinked to original sources

arXiv2023

Implementing a Metropolis sampler on decomposable graphs using a variety of ways to represent the graph

We describe the implementation of the Giudici-Green Metropolis sampling method for decomposable graphs using a variety of structures to represent the graph. These comprise the graph itself, the Junction tree, the Almond tree and the Ibarra clique-separator graph. For each structure, we describe the process for ascertaining whether adding or deleting a specific edge results in a new graph that is also decomposable, and the updates that need to be made to the structure if the edge perturbation is made. For the Almond tree and Ibarra graph these procedures are novel. We find that using the graph itself is generally at least competitive in terms of computational efficiency for a variety of graph distributions, but note that the other structures may allow and suggest samplers using different perturbations with lower rejection rates and/or better mixing properties. The sampler has applications in estimating graphical models for systems of multivariate Gaussian or Multinomial variables.

stat.CO↗

arXiv2017

A structural Markov property for decomposable graph laws that allows control of clique intersections

We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques, so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.

stat.CO↗

arXiv2012

Sampling decomposable graphs using a Markov chain on junction trees

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology for such inference, by making two contributions to the computational geometry of decomposable graphs. The first of these provides sufficient conditions under which it is possible to completely connect two disconnected complete subsets of vertices, or perform the reverse procedure, yet maintain decomposability of the graph. The second is a new Markov chain Monte Carlo sampler for arbitrary positive distributions on decomposable graphs, taking a junction tree representing the graph as its state variable. The resulting methodology is illustrated with numerical experiments on three specific models.

stat.CO↗

arXiv2003

On the structure of proten-protein interaction networks

We present a simple model for the underlying structure of protein-protein pairwise interaction graphs that is based on the way in which proteins attach to each other in experiments such as yeast two-hybrid assays. We show that data on the interactions of human proteins lend support to this model. The frequency of the number of connections per protein under this model does not follow a power law, in contrast to the reported behaviour of data from large scale yeast two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs from the underlying graphs generated with our model, in a way analogous to the sampling performed in large scale yeast two-hybrid searches, gives degree distributions that differ subtly from the power law and that fit the observed data better than the power law itself. Our results show that the observation of approximate power law behaviour in a sampled sub-graph does not imply that the underlying graph follows a power law.

q-bio.MN↗