18,562 research outputs found
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey
Dynamic networks are used in a wide range of fields, including social network
analysis, recommender systems, and epidemiology. Representing complex networks
as structures changing over time allow network models to leverage not only
structural but also temporal patterns. However, as dynamic network literature
stems from diverse fields and makes use of inconsistent terminology, it is
challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a
lot of attention in recent years for their ability to perform well on a range
of network science tasks, such as link prediction and node classification.
Despite the popularity of graph neural networks and the proven benefits of
dynamic network models, there has been little focus on graph neural networks
for dynamic networks. To address the challenges resulting from the fact that
this research crosses diverse fields as well as to survey dynamic graph neural
networks, this work is split into two main parts. First, to address the
ambiguity of the dynamic network terminology we establish a foundation of
dynamic networks with consistent, detailed terminology and notation. Second, we
present a comprehensive survey of dynamic graph neural network models using the
proposed terminologyComment: 28 pages, 9 figures, 8 table
Statistical clustering of temporal networks through a dynamic stochastic block model
Statistical node clustering in discrete time dynamic networks is an emerging
field that raises many challenges. Here, we explore statistical properties and
frequentist inference in a model that combines a stochastic block model (SBM)
for its static part with independent Markov chains for the evolution of the
nodes groups through time. We model binary data as well as weighted dynamic
random graphs (with discrete or continuous edges values). Our approach,
motivated by the importance of controlling for label switching issues across
the different time steps, focuses on detecting groups characterized by a stable
within group connectivity behavior. We study identifiability of the model
parameters, propose an inference procedure based on a variational expectation
maximization algorithm as well as a model selection criterion to select for the
number of groups. We carefully discuss our initialization strategy which plays
an important role in the method and compare our procedure with existing ones on
synthetic datasets. We also illustrate our approach on dynamic contact
networks, one of encounters among high school students and two others on animal
interactions. An implementation of the method is available as a R package
called dynsbm
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Latent space models for multidimensional network data
Network data are any relational data recorded among a group of individuals, the nodes. When multiple relations are recorded among the same set of nodes, a more complex object arises, which we refer to as “multidimensional network”, or
“multiplex”, where different relations corresponding to different networks. In the past, statistical analysis of networks has mainly focused on single-relation network data, referring to a single relation of interest. Only in recent years statistical
models specifically tailored for multiplex data begun to be developed. In this context, only a few works have been introduced in the literature with the aim at extending the latent space modeling framework to multiplex data. Such framework postulates
that nodes may be characterized by latent positions in a p-dimensional Euclidean space and that the presence/absence of an edge between any two nodes depends on such positions. When considering multidimensional network data, latent space
models can help capture the associations between the nodes and summarize the observed structure in the different networks composing a multiplex. This dissertation discusses some latent space models for multidimensional network
data, to account for different features that observed multiplex data may present. A first proposal allows to jointly represent the different networks into a single latent space, so that average similarities between the nodes may be captured as
proximities in such space. A second work introduces a class of latent space models with node-specific effects, in order to deal with different degrees of heterogeneity within and between networks in multiplex data, corresponding to different types
of node-specific behaviours. A third work addresses the issue of clustering of the nodes in the latent space, a frequently observed feature in many real world network and multidimensional network data. Here, clusters of nodes in the latent space
correspond to communities of nodes in the multiplex. The proposed models are illustrated both via simulation studies and real world applications, to study their perfomances and abilities
Topics in social network analysis and network science
This chapter introduces statistical methods used in the analysis of social
networks and in the rapidly evolving parallel-field of network science.
Although several instances of social network analysis in health services
research have appeared recently, the majority involve only the most basic
methods and thus scratch the surface of what might be accomplished.
Cutting-edge methods using relevant examples and illustrations in health
services research are provided
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