Title: Estimation of Time Varying Networks Using Latent Dynamics
Advisor: Professor George Michailidis, Associate Professor Yves Atchade
Committee Members: Professor Xuming He
Abstract: In Modern days world many complex systems are represented through networks. Networks are capable of capturing dependence relationships and have been extensively employed in diverse scientific fields such as biology, social sciences etc. Recently the focus has been on studying time varying networks due to increased availability of relevant data. Their study reveals the organizational structure of the underlying process and also its dynamics. Examples include gene regulatory networks, understanding stock markets, protein-protein interaction within the cell etc. The problem that we are interested here is to estimate the structure of the high-dimensional networks that are varying over time. The key contributions in this project come in two different areas, one in the modeling approach and other in using a non-standard block coordinate descent algorithm to estimate the structure of the 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 the locations of the nodes in a latent space. As far as the methodology is concerned we use a penalized pseudo-likelihood method to estimate the structure of the network. The performance of the proposed methodology is assessed through a set of simulation studies and we also discuss the strategy for proving the convergence of the algorithm.