Robust Gaussian Graphical Modeling Via $L_1$ Penalization

• Activity Number: 589
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Hongzhe Li*+
• Companies: University of Pennsylvania
• Keywords: High dimensional statistics ; Genetic Network ; Graphical Model ; Variable selection ; Robust

Abstract

Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a $l_1$ penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso.