Structural Models of Network Contacts Between Actors Governed by Activity and Attraction
(2013) Abstract
 This thesis consists of five papers on the subject of statistical modeling of stochastic networks. The NGmodel proposed in Paper I combines a block structure with parameters that capture the identities of vertices and thus the new approach stresses the concept of egonets, which describes the structure around identified vertices. The models proposed in Papers IIV are closely related to the NGmodel proposed in Paper I.
In Paper I, we propose a parametric digraph model which models network data utilizing vertex group memberships and the identities of vertices, namely the NGmodel of independent outnets. We present estimation methods based on the EM algorithm for the parameter estimations and the recovery of latent... (More)  This thesis consists of five papers on the subject of statistical modeling of stochastic networks. The NGmodel proposed in Paper I combines a block structure with parameters that capture the identities of vertices and thus the new approach stresses the concept of egonets, which describes the structure around identified vertices. The models proposed in Papers IIV are closely related to the NGmodel proposed in Paper I.
In Paper I, we propose a parametric digraph model which models network data utilizing vertex group memberships and the identities of vertices, namely the NGmodel of independent outnets. We present estimation methods based on the EM algorithm for the parameter estimations and the recovery of latent group memberships. A companion model (the reversed NGmodel) is also introduced which reverses the parameterization of the NGmodel. We apply both models to directed social networks.
In Paper II, we study an undirected version of the NGmodel and investigate parameter estimation and latent group membership recovery techniques. We apply the methods to model undirected social networks.
In Paper III, we study various probabilistic properties of the NGmodel introduced in Paper I. We propose a similarity matrix as a tool for comparing actors' egonets and discuss its probabilistic properties. We propose several clustering coefficients, whose probabilistic properties are investigated in the NGmodel setting.
In Paper IV, we propose two models as extensions of the NGmodel by incorporating the effect of actors' attributes (covariates) into the modeling of network data. We propose algorithms for the parameter estimation and the recovery of latent group memberships. We apply the models to both simulated and real networks.
In Paper V, we propose a parametric digraph model conditioned on given sequence of vertex outdegrees by utilizing the parameterization of the reversed NGmodel proposed in Paper I. We derive the form of the probability function and the marginal distributions. We propose parameter estimation methods and methods for drawing samples from the distribution of the conditional model. We investigate several probabilistic properties of the parameter estimates and present examples of applications of the model to both simulated and real network data. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3738645
 author
 Geng, Zhi
 supervisor
 opponent

 Professor Karoński, Michał, Department of Discrete Mathematics, Adam Mickiewicz university
 organization
 publishing date
 2013
 type
 Thesis
 publication status
 published
 subject
 keywords
 Directed graph, Egonets, EM algorithm, Gibbs sampling, Multinomial distribution, Hypergeometric distribution, Vertex covariates, Clustering coefficient, Taylor expansion
 pages
 201 pages
 defense location
 EC3:207, Holger Crafoords, Ekonomicentrum
 defense date
 20130608 10:15
 ISBN
 9789174735529
 language
 English
 LU publication?
 yes
 id
 c4cc06da13c44d6bbf91809350972fe2 (old id 3738645)
 date added to LUP
 20130517 11:16:17
 date last changed
 20160919 08:45:16
@misc{c4cc06da13c44d6bbf91809350972fe2, abstract = {This thesis consists of five papers on the subject of statistical modeling of stochastic networks. The NGmodel proposed in Paper I combines a block structure with parameters that capture the identities of vertices and thus the new approach stresses the concept of egonets, which describes the structure around identified vertices. The models proposed in Papers IIV are closely related to the NGmodel proposed in Paper I.<br/><br> <br/><br> In Paper I, we propose a parametric digraph model which models network data utilizing vertex group memberships and the identities of vertices, namely the NGmodel of independent outnets. We present estimation methods based on the EM algorithm for the parameter estimations and the recovery of latent group memberships. A companion model (the reversed NGmodel) is also introduced which reverses the parameterization of the NGmodel. We apply both models to directed social networks.<br/><br> <br/><br> In Paper II, we study an undirected version of the NGmodel and investigate parameter estimation and latent group membership recovery techniques. We apply the methods to model undirected social networks. <br/><br> <br/><br> In Paper III, we study various probabilistic properties of the NGmodel introduced in Paper I. We propose a similarity matrix as a tool for comparing actors' egonets and discuss its probabilistic properties. We propose several clustering coefficients, whose probabilistic properties are investigated in the NGmodel setting. <br/><br> <br/><br> In Paper IV, we propose two models as extensions of the NGmodel by incorporating the effect of actors' attributes (covariates) into the modeling of network data. We propose algorithms for the parameter estimation and the recovery of latent group memberships. We apply the models to both simulated and real networks.<br/><br> <br/><br> In Paper V, we propose a parametric digraph model conditioned on given sequence of vertex outdegrees by utilizing the parameterization of the reversed NGmodel proposed in Paper I. We derive the form of the probability function and the marginal distributions. We propose parameter estimation methods and methods for drawing samples from the distribution of the conditional model. We investigate several probabilistic properties of the parameter estimates and present examples of applications of the model to both simulated and real network data.}, author = {Geng, Zhi}, isbn = {9789174735529}, keyword = {Directed graph,Egonets,EM algorithm,Gibbs sampling,Multinomial distribution,Hypergeometric distribution,Vertex covariates,Clustering coefficient,Taylor expansion}, language = {eng}, pages = {201}, title = {Structural Models of Network Contacts Between Actors Governed by Activity and Attraction}, year = {2013}, }