Estimating Latent Space Models for Network Data with Multivariate Response Variables

• Activity Number: 307 - Novel Approaches for Analyzing Dynamic Networks
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xuefei Zhang* and Ji Zhu and Gongjun Xu
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: network data analysis; latent space models

Abstract

Network latent space models assume that each node is associated with an unobserved latent position in a Euclidean space, and such latent variables determine the probability of two nodes connecting with each other. In many applications, each node in the network is also observed with a set of response variables of interest. In this paper, we propose a joint latent space model where the latent variables not only explain the network structure, but also are informative for the response variables. We develop a projected gradient descent algorithm that jointly estimates the latent positions using a criterion incorporating both the network structure and the node responses. We provide a theoretical guarantee that incorporating node response variables could improve the estimation accuracy of the latent positions and demonstrate it by simulation. We also show that the joint estimation leads to improvements in downstream tasks, such as responses missing value imputation, by simulation and application to real data examples.