TY - BOOK

T1 - The autoregressive stochastic block model with changes in structure

AU - Ludkin, Matthew Robert

PY - 2017

Y1 - 2017

N2 - Network science has been a growing subject for the last three decades, with sta-tistical analysis of networks seing an explosion since the advent of online socialnetworks. An important model within network analysis is the stochastic blockmodel, which aims to partition the set of nodes of a network into groups whichbehave in a similar way. This thesis proposes Bayesian inference methods forproblems related to the stochastic block model for network data. The presentedresearch is formed of three parts. Firstly, two Markov chain Monte Carlo samplersare proposed to sample from the posterior distribution of the number of blocks,block memberships and edge-state parameters in the stochastic block model. Theseallow for non-binary and non-conjugate edge models, something not considered inthe literature.Secondly, a dynamic extension to the stochastic block model is presented whichincludes autoregressive terms. This novel approach to dynamic network modelsallows the present state of an edge to influence future states, and is therefore namedthe autoregresssive stochastic block model. Furthermore, an algorithm to performinference on changes in block membership is given. This problem has gained someattention in the literature, but not with autoregressive features to the edge-statedistribution as presented in this thesis.Thirdly, an online procedure to detect changes in block membership in the au-toregresssive stochastic block model is presented. This allows networks to bemonitored through time, drastically reducing the data storage requirements. Ontop of this, the network parameters can be estimated together with the block memberships.Finally, conclusions are drawn from the above contributions in the context ofthe network analysis literature and future directions for research are identified.

AB - Network science has been a growing subject for the last three decades, with sta-tistical analysis of networks seing an explosion since the advent of online socialnetworks. An important model within network analysis is the stochastic blockmodel, which aims to partition the set of nodes of a network into groups whichbehave in a similar way. This thesis proposes Bayesian inference methods forproblems related to the stochastic block model for network data. The presentedresearch is formed of three parts. Firstly, two Markov chain Monte Carlo samplersare proposed to sample from the posterior distribution of the number of blocks,block memberships and edge-state parameters in the stochastic block model. Theseallow for non-binary and non-conjugate edge models, something not considered inthe literature.Secondly, a dynamic extension to the stochastic block model is presented whichincludes autoregressive terms. This novel approach to dynamic network modelsallows the present state of an edge to influence future states, and is therefore namedthe autoregresssive stochastic block model. Furthermore, an algorithm to performinference on changes in block membership is given. This problem has gained someattention in the literature, but not with autoregressive features to the edge-statedistribution as presented in this thesis.Thirdly, an online procedure to detect changes in block membership in the au-toregresssive stochastic block model is presented. This allows networks to bemonitored through time, drastically reducing the data storage requirements. Ontop of this, the network parameters can be estimated together with the block memberships.Finally, conclusions are drawn from the above contributions in the context ofthe network analysis literature and future directions for research are identified.

KW - Networks

KW - statistics

KW - Stochastic block model

U2 - 10.17635/lancaster/thesis/296

DO - 10.17635/lancaster/thesis/296

M3 - Doctoral Thesis

PB - Lancaster University

ER -