Robust Estimation in Large Gaussian Graphical Model

• Activity Number: 129
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Peng Tang*+ and Huijing Jiang and Xinwei Deng
• Companies: Georgia Institute of Technology and IBM T. J. Watson Research Center and Virginia Tech
• Keywords: covariance matrix inverse ; sparse graphical model ; robust estimation ; L2E ; graphical lasso

Abstract

Graphical models provide a useful framework to represent and exploit conditional independence structures among multiple variables. Under the assumption of multivariate Gaussian distribution, the problem of estimating undirected graphical models can be translated into regularization of inverse covariance matrices. However, due to the curse of dimensionality,the influence of outliers increases at exponential rate of dimensionality. In this paper, we proposed a series of estimators of inverse covariance matrix based on the integrated squared error criterion (ISE). ISE is a nonparametric criterion, which seeks to find the largest portion of the data that "matches" the model. Therefore, our proposed estimators are more resistent to the outliers compared with likelihood based approaches. Moreover, we encourage the sparsity by adding L1 (lasso) penalty in the objective function. Extensive numerical simulations are constructed to compare the performance of our proposed methods with some existing approaches under varying settings of outliers. We further demonstrate the strength of our method through its application on a gene expression data set to infer genetic network.