L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression

Sparse learning in high-dimensional survival analysis is of great practical importance, as exemplified by modern applications in credit risk analysis and high-throughput genomic data analysis. In this article, we consider the L 0 -regularized learning for simultaneous variable selection and estimation under the framework of additive hazards models and utilize the idea of primal dual active sets to develop an algorithm targeted at solving the traditionally nonpolynomial time optimization problem. Under interpretable conditions, comprehensive statistical properties, including model selection consistency, oracle inequalities under various estimation losses, and the oracle property, are established for the global optimizer of the proposed approach. Moreover, our theoretical analysis for the algorithmic solution reveals that the proposed L 0 -regularized learning can be more efficient than other regularization methods in that it requests a smaller sample size as well as a lower minimum signal strength to identify the significant features. The effectiveness of the proposed method is evidenced by simulation studies and real-data analysis. Summary of Contribution: Feature selection is a fundamental statistical learning technique under high dimensions and routinely encountered in various areas, including operations research and computing. This paper focuses on the L 0 -regularized learning for feature selection in high-dimensional additive hazards regression. The matching algorithm for solving the nonconvex L 0 -constrained problem is scalable and enjoys comprehensive theoretical properties.