Nested exemplar latent space models for dimension reduction in dynamic networks

Music City Center 

Dynamic latent space models are widely used for characterizing changes in networks and
relational data over time. These models assign to each node latent attributes that characterize
connectivity with other nodes, with these latent attributes dynamically changing over time. Node 25
attributes can be organized as a three-way tensor with modes corresponding to nodes, latent
space dimension, and time. Unfortunately, as the number of nodes and time points increases, the
number of elements of this tensor becomes enormous, leading to computational and statistical
challenges, particularly when data are sparse. We propose a new approach for massively reducing
dimensionality by expressing the latent node attribute tensor as low rank. This leads to an 30
interesting new nested exemplar latent space model, which characterizes the node attribute
tensor as dependent on low-dimensional exemplar traits for each node, weights for each latent
space dimension, and exemplar curves characterizing time variation. We study properties of
this framework, including expressivity, and develop efficient Bayesian inference algorithms. The
approach leads to substantial advantages in simulations and

latent factor model

dynamic network

Bayesian nonparametrics

ecology

tensor factorization 

Section on Bayesian Statistical Science