Latent Modeling of Dynamic Social Networks

Restricted (Penn State Only)
Author:
Kim, Bomin
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 12, 2018
Committee Members:
  • David Russell Hunter, Dissertation Advisor
  • David Russell Hunter, Committee Chair
  • Jia Li, Committee Member
  • Lin Lin, Committee Member
  • Bruce A Desmarais Jr., Outside Member
  • Xiaoyue Niu, Dissertation Advisor
  • Xiaoyue Niu, Committee Chair
Keywords:
  • dynamic networks
  • latent space model
  • social network analysis
  • survival modeling
  • Bayesian statistics
Abstract:
In this dissertation, we present statistical methods for modeling dynamic social networks, with the goal of jointly investigating the observed features and unobserved structure of the data and their temporal evolutions using latent variables. We develop three dynamic network models which not only provide theoretical contributions to the area of statistical network modeling, but also exhibit high practicality and interpretability for real-world applications in social science domains. First, the dynamic additive and multiplicative effects (DAME) model is a statistical regression model for a sequence of time-varying matrices that are correlated over time. The DAME model employs eigen-decompositions such that the model can represent a wide array of patterns via unrestricted low-rank approximation. In addition, temporal evolution of the network is modeled through Gaussian processes, which capture temporal dependences in long memory history beyond the Markov property. Next, we propose a point process model with latent positions---a continuous-time network model that uses both temporal and socio-spatial components of the data. Built upon the Cox multiplicative intensity model, our point process model investigates which traits and behaviors are predictive of future interpersonal interaction, while additionally integrate the latent space model into stochastic intensity terms in order to explore the statistical uncertainty in the latent social space. Lastly, we introduce the hyperedge event model (HEM), which is a generative model for events that can be represented as directed edges with one sender and one or more receivers or one receivers and one or more senders. We incorporate both an edge-formation equation and a timing equation into the model specification to jointly understand who interacts with whom, and when. The HEM offers some innovations by extending a growing class of dynamic network models for hyperedges and providing flexible choice of distributions for event timing.