46,751 research outputs found
A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market
We propose a dynamic network model where two mechanisms control the
probability of a link between two nodes: (i) the existence or absence of this
link in the past, and (ii) node-specific latent variables (dynamic fitnesses)
describing the propensity of each node to create links. Assuming a Markov
dynamics for both mechanisms, we propose an Expectation-Maximization algorithm
for model estimation and inference of the latent variables. The estimated
parameters and fitnesses can be used to forecast the presence of a link in the
future. We apply our methodology to the e-MID interbank network for which the
two linkage mechanisms are associated with two different trading behaviors in
the process of network formation, namely preferential trading and trading
driven by node-specific characteristics. The empirical results allow to
recognise preferential lending in the interbank market and indicate how a
method that does not account for time-varying network topologies tends to
overestimate preferential linkage.Comment: 19 pages, 6 figure
Joint Structure Learning of Multiple Non-Exchangeable Networks
Several methods have recently been developed for joint structure learning of
multiple (related) graphical models or networks. These methods treat individual
networks as exchangeable, such that each pair of networks are equally
encouraged to have similar structures. However, in many practical applications,
exchangeability in this sense may not hold, as some pairs of networks may be
more closely related than others, for example due to group and sub-group
structure in the data. Here we present a novel Bayesian formulation that
generalises joint structure learning beyond the exchangeable case. In addition
to a general framework for joint learning, we (i) provide a novel default prior
over the joint structure space that requires no user input; (ii) allow for
latent networks; (iii) give an efficient, exact algorithm for the case of time
series data and dynamic Bayesian networks. We present empirical results on
non-exchangeable populations, including a real data example from biology, where
cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference
on Artificial Intelligence and Statistics (AISTATS
Locally Adaptive Dynamic Networks
Our focus is on realistically modeling and forecasting dynamic networks of
face-to-face contacts among individuals. Important aspects of such data that
lead to problems with current methods include the tendency of the contacts to
move between periods of slow and rapid changes, and the dynamic heterogeneity
in the actors' connectivity behaviors. Motivated by this application, we
develop a novel method for Locally Adaptive DYnamic (LADY) network inference.
The proposed model relies on a dynamic latent space representation in which
each actor's position evolves in time via stochastic differential equations.
Using a state space representation for these stochastic processes and
P\'olya-gamma data augmentation, we develop an efficient MCMC algorithm for
posterior inference along with tractable procedures for online updating and
forecasting of future networks. We evaluate performance in simulation studies,
and consider an application to face-to-face contacts among individuals in a
primary school
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