Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

• Activity Number: 570
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Shengchun Kong*+ and Bin Nan
• Companies: University of Michigan and University of Michigan
• Keywords: Cox regression ; finite sample ; lasso ; oracle inequality ; variable selection

Abstract

We consider the finite sample properties of the regularized highdimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz. We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulty caused by the lack of iid and Lipschitz property.