Sparse Covariance Estimation in Graphical Models

• Activity Number: 599
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kshitij Khare*+
• Companies: University of Florida

Abstract

We consider the problem of covariance estimation in high dimensional settings when the graph $G$ is either given or is unknown. Sparse estimation of covariance matrices gives rise to models known as graphical models. These models can be represented as networks or graphs, where the nodes represent random variables and edges represent their interactions. When the random variables are jointly Gaussian distributed, the lack of edges in such graphs can be interpreted as conditional and/or marginal independencies between these variables. We present a likelihood based approach to high dimensional covariance estimation which builds sparse graphical models and leads to consistent covariance estimation. We study the theoretical properties of our procedure and proceed to illustrate our approach on both simulated and real data.