Maximum Likelihood Estimation of a Directed Acyclic Gaussian Graph

• Activity Number: 399
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yiping Yuan and Xiaotong Shen*+ and Wei Pan
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: Directed acyclic graph ; nonconvex ; gene networks

Abstract

Directed acyclic graphs have been widely used to describe causal relations among interacting units. Estimation of a directed acyclic graph presents a great challenge without prior knowledge about the order of interacting units, where the number of enumeration of potential directions grows super-exponentially. A traditional method usually estimates directions locally and sequentially, and hence results in biased estimation. In this paper, we propose a global approach to determine all directions simultaneously, through constrained maximum likelihood with nonconvex constraints reinforcing a directed acyclic graph requirement. Computationally, we propose an efficient algorithm based on a projection-based accelerated gradient method and difference convex programming for approximating nonconvex constrained sets. Numerically, we demonstrate that the method leads to accurate parameter estimation, in parameter estimation as well as identifying graphical structures. Moreover, an application to gene network analysis will be described.