21 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
On sparsity, power-law and clustering properties of graphex processes
This paper investigates properties of the class of graphs based on
exchangeable point processes. We provide asymptotic expressions for the number
of edges, number of nodes and degree distributions, identifying four regimes:
(i) a dense regime, (ii) a sparse almost dense regime, (iii) a sparse regime
with power-law behaviour, and (iv) an almost extremely sparse regime. We show
that under mild assumptions, both the global and local clustering coefficients
converge to constants which may or may not be the same. We also derive a
central limit theorem for the number of nodes. Finally, we propose a class of
models within this framework where one can separately control the latent
structure and the global sparsity/power-law properties of the graph
Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data
We propose a novel class of network models for temporal dyadic interaction
data. Our goal is to capture a number of important features often observed in
social interactions: sparsity, degree heterogeneity, community structure and
reciprocity. We propose a family of models based on self-exciting Hawkes point
processes in which events depend on the history of the process. The key
component is the conditional intensity function of the Hawkes Process, which
captures the fact that interactions may arise as a response to past
interactions (reciprocity), or due to shared interests between individuals
(community structure). In order to capture the sparsity and degree
heterogeneity, the base (non time dependent) part of the intensity function
builds on compound random measures following Todeschini et al. (2016). We
conduct experiments on a variety of real-world temporal interaction data and
show that the proposed model outperforms many competing approaches for link
prediction, and leads to interpretable parameters