33,934 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
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
Efficient inference of overlapping communities in complex networks
We discuss two views on extending existing methods for complex network
modeling which we dub the communities first and the networks first view,
respectively. Inspired by the networks first view that we attribute to White,
Boorman, and Breiger (1976)[1], we formulate the multiple-networks stochastic
blockmodel (MNSBM), which seeks to separate the observed network into
subnetworks of different types and where the problem of inferring structure in
each subnetwork becomes easier. We show how this model is specified in a
generative Bayesian framework where parameters can be inferred efficiently
using Gibbs sampling. The result is an effective multiple-membership model
without the drawbacks of introducing complex definitions of "groups" and how
they interact. We demonstrate results on the recovery of planted structure in
synthetic networks and show very encouraging results on link prediction
performances using multiple-networks models on a number of real-world network
data sets
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