Penalized Estimation of Sparse High-Dimensional--Directed Acyclic Graphs

• Activity Number: 145
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): George Michailidis*+
• Companies: University of Michigan
• Keywords: Estimation ; Directed Acyclic Graphs ; Penalized methods

Abstract

Directed acyclic graphs (DAGs) arise naturally in biological systems, where directed edges between nodes represent in?uences of com- ponents of systems on each other. The general problem of estimating DAGs from observed data is NP-hard. We study the problem of estimating DAGs when the nodes exhibit a natural ordering, so that it reduces to that of estimating the structure of the network. We propose a penalized likelihood approach that directly estimates the adjacency matrix of DAGs. Both lasso and adaptive lasso penalties are considered and an efficient algorithm is proposed for estimation of high dimensional DAGs. We study their theoretical properties and apply them to a transcription regulatory network. Extension to Granger causality is also considered.