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

TL;DR

This paper establishes non-asymptotic oracle inequalities for high-dimensional Cox regression with Lasso penalty, addressing challenges posed by non-iid and non-Lipschitz loss functions in survival analysis.

Contribution

It introduces a novel approach to derive finite-sample bounds for Cox regression, overcoming the limitations of existing methods that assume iid and Lipschitz conditions.

Findings

Derived non-asymptotic oracle inequalities for Cox regression

Addressed non-iid and non-Lipschitz challenges in survival data

Provided theoretical guarantees for Lasso-penalized Cox models

Abstract

We consider the finite sample properties of the regularized high-dimensional 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.