On Estimation and Inference in Latent Structure Random Graphs

Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learning

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or discrete assumptions, which are restrictive under many applications. In this...

Bayesian Inference on Latent Structure in Time Series

A range of developments in Bayesian time series modelling in recent years has focussed on issues of identifying latent structure in time series. This has led to new uses and interpretations of existing theory for latent process decompositions of dynamic models, and to new models for univariate and multivariate time series. This article draws together concepts and modelling approaches that are c...

Latent Voter Model on Locally Tree-Like Random Graphs

In the latent voter model, which models the spread of a technology through a social network, individuals who have just changed their choice have a latent period, which is exponential with rate λ, during which they will not buy a new device. We study site and edge versions of this model on random graphs generated by a configuration model in which the degrees d(x) have 3 ≤ d(x) ≤M . We show that ...

Topics in random graphs, combinatorial optimization, and statistical inference

Bipodal structure in oversaturated random graphs

We study the asymptotics of large simple graphs constrained by the limiting density of edges and the limiting subgraph density of an arbitrary fixed graph H. We prove that, for all but finitely many values of the edge density, if the density of H is constrained to be slightly higher than that for the corresponding Erdős-Rényi graph, the typical large graph is bipodal with parameters varying ana...