148 research outputs found
Bayesian nonparametrics for Sparse Dynamic Networks
We propose a Bayesian nonparametric prior for time-varying networks. To each
node of the network is associated a positive parameter, modeling the
sociability of that node. Sociabilities are assumed to evolve over time, and
are modeled via a dynamic point process model. The model is able to (a) capture
smooth evolution of the interaction between nodes, allowing edges to
appear/disappear over time (b) capture long term evolution of the sociabilities
of the nodes (c) and yield sparse graphs, where the number of edges grows
subquadratically with the number of nodes. The evolution of the sociabilities
is described by a tractable time-varying gamma process. We provide some
theoretical insights into the model and apply it to three real world datasets.Comment: 10 pages, 8 figure
Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models
W-graph refers to a general class of random graph models that can be seen as
a random graph limit. It is characterized by both its graphon function and its
motif frequencies. In this paper, relying on an existing variational Bayes
algorithm for the stochastic block models along with the corresponding weights
for model averaging, we derive an estimate of the graphon function as an
average of stochastic block models with increasing number of blocks. In the
same framework, we derive the variational posterior frequency of any motif. A
simulation study and an illustration on a social network complete our work
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