Measurement Error Correction in High-Dimensional GLMs

• Activity Number: 366
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Øystein Sørensen*+ and Arnoldo Frigessi and Magne Thoresen
• Companies: Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo and Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo and Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo
• Keywords: Measurement error ; Errors-in-variables ; Matrix Uncertainty Selector ; Generalized linear model

Abstract

Regularization schemes like the Lasso or Dantzig Selector (DS) are widely used for model selection when p>>n. In their standard formulations, these methods assume that the covariates are perfectly observed, although in many cases they may be subject to measurement error. It has been shown that the Lasso or DS may be severely affected by measurement error, in particular yielding too large models. To account for this, Rosenbaum and Tsybakov (R&T, 2010) proposed the Matrix Uncertainty Selector (MUS) for linear regression, a modification of the DS which remarkably does not require an estimate of the measurement error distribution. In this paper, we propose a Generalized MUS (GMUS) for generalized linear models (GLMs). Like the MUS, it does not require an estimate of the measurement error distribution, and it is computationally tractable. We apply GMUS to detect differentially expressed genes in classification problems with microarray data. As noted by R&T for linear models, a Lasso analog of the GMUS can also be defined. We compare both methods to the original Lasso and DS, and discuss the choice of regularization parameters.