Robust Gaussian Graphical Lasso

• Activity Number: 682
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Hokeun Sun*+
• Companies: University of Pennsylvania
• Keywords: Robust estimation ; Graphical Lasso ; coordinate gradient descent ; Biological Network

Abstract

We propose a sparse Gaussian graphical model 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. Penalizing the likelihood by Lasso penalty, we estimate a sparse inverse covariance matrix. The coordinate gradient descent algorithm is applied to obtain the minimizer of the penalized likelihood, where nonzero elements represent network edges among nodes. Based on this covariance selection model, we re-estimate the positive definite concentration matrix for more accurate estimation, using the iterative proportional fitting algorithm. In simulation study we demonstrate that the proposed robust method performs much better than the ordinary Gaussian graphical model in terms of both selection and estimation when outliers are present.