B1278
Title: Latent space models for multiplex networks with shared structure
Authors: Liza Levina - University of Michigan (United States) [presenting]
Abstract: Statistical tools for analysing a single network are now widely available, but many practical settings involve multiple networks. These can arise as a sample of networks (for example, brain connectivity networks for a sample of patients), a single network with multiple types of edges (for example, trade between countries in many different commodities), or a single network evolving over time. The term multiplex networks refers to multiple and generally heterogeneous networks observed on the same shared node set; the two examples above are multiplex networks. A new latent space model is proposed for multiplex networks, which answers a key question of what part of the underlying structure is shared between all the networks and what is unique to each one. The model learns from data and pools information adaptively. Identifiability is established, and a fitting procedure is developed using convex optimization combined with a nuclear norm penalty, proving a recovery guarantee for the latent positions as long as sufficient separation between the shared and the individual latent subspaces exists. The model is compared to competing methods in the literature on simulated and multiplex networks, describing the worldwide trade of agricultural products.
