Estimation of Time-Varying Networks Using Latent Dynamics

• Activity Number: 254
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sandipan Roy*+ and Yves Atchade and George Michailidis
• Companies: University of Michigan and Statistics Department, University of Michigan and University of Michigan
• Keywords: high-dimensional networks ; dynamics ; pseudo-likelihood ; block coordinate descent ; iterated filtering

Abstract

Networks changing their structure over time can be used to represent dependence relationships among entities in a dynamic system such as living cells or social communities. There has been a lot of work for the past couple of years on estimating time-invariant high-dimensional networks but there is less work on modeling dynamic networks. We introduce a novel modeling approach for tracking the dynamics of a time-varying network. We model the time-varying relationships between the nodes as a composition of a fixed factor and a time-varying factor where the latter is controlled by a latent process that induces the changes in the locations of the nodes over time. Further we assume that the underlying latent process is stationary so that we can combine information across time and estimate the network structure effectively. As far as the methodology is concerned, we use penalized pseudo-likelihood method and introduce a non standard block coordinate descent algorithm based on ideas from importance sampling and iterated filtering. The performance of the proposed methodology is assessed on synthetic data and we discuss some properties of the algorithm as well.