Joint Adaptive Gaussian Graphical Method for Unbalanced Multi-Classes

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Liang Shan*+ and Inyoung Kim
• Companies: Virginia Tech and Virginia Tech
• Keywords: Gene network exploration ; high-dimensional ; joint adaptive graphical lasso ; small sample size ; unequal sample size

Abstract

In this paper, we consider the problem of estimating multi-Class Gaussian graphical models in high dimensional data with unbalanced multi-classes. Most existing methods require equal sample size or similar sample size among classes. However, many of real application do not have similar sample size. Hence, in this paper, we incorporate unequal sample sizes into multi-class Gaussian graphical model and develop the Joint Adaptive Graphical Lasso, a weighted L1 penalized approach, which also combines information across classes so that their common characteristics could be shared during the estimation process. We also combine resampling approach with BIC type criteria to choose the regularization parameter. We show that our approach performs better than existing methods in terms of information loss, false positive rate, and false negative rate. We demonstrate the advantage of our approach using genetic pathway expression data.