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Abstract Details

Activity Number: 570
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #305384
Title: Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso
Author(s): Shengchun Kong*+ and Bin Nan
Companies: University of Michigan and University of Michigan
Address: 4794 Washtenaw Ave., Ann Arbor, MI, 48108, United States
Keywords: Cox regression ; finite sample ; lasso ; oracle inequality ; variable selection

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.

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