Multi-Layered Networks Estimation with Penalized Maximum Likelihood

• Activity Number: 551
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Jiahe Lin* and Sumanta Basu and George Michailidis and Moulinath Banerjee
• Companies: and University of Michigan and University of Florida and University of Michigan
• Keywords: maximum likelihood ; co-ordinate descent ; Gaussian graphical models

Abstract

Networks are one of the most popular tools for capturing the interactions between nodes, which are used to represent the underlying random variables. In particular, constructing and analyzing a layered structure provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We propose a new unified approach for estimating multi-layered networks. The proposed method offers an efficient way of estimating edges between and across layers iteratively, by constructing an objective function based on the penalized joint maximum likelihood function (under a Gaussianity assumption), then using block co-ordinate descent to do the optimization. Our method decouples the estimation of undirected and directed edges within each iteration, however the updated estimates are integrated in the next iteration. The performance of the methodology is illustrated via simulations. This is joint work with Sumanta Basu, George Michailidis and Moulinath Banerjee.