Estimation of Sparse Directed Acyclic Graphs Through a Penalized Likelihood

• 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): Sung Won Han*+ and Hua Zhong and Gong Chen and Belousov Anton and Laurent Essioux
• Companies: Hoffmann-La Roche / New York University and New York University and Hoffmann-La Roche Inc. and Hoffmann-La Roche Inc. and Hoffmann-La Roche Inc.
• Keywords: Directed acyclic graph ; Penalized likelihood estimation ; Non-homogeneous latent variables ; Unknown natural ordering ; Lasso estimation

Abstract

Directed acyclic graphic model has been suggested to model the interactions among random variables where directed edges represent the causal influence of components of the system. In this paper, we discuss a linear latent variable approach to model the adjacency matrix of directed acyclic graphs and estimate it via a penalized profile-likelihood method based on multivariate normal distributions. Since we allow for unequal variance of the latent variables to account for noisy data and we assume that structure order is unknown, the estimation of the optimal adjacency matrix is burdensome. Thus, we propose a heuristic algorithm, which splits the main optimization problem into inner and outer sub-problems conditional on the network structure. We demonstrate the application of this method in constructing gene regulatory networks, and compare the results from the networks.