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Title: Estimation in the high dimensional additive hazard model with l0 type of penalty Authors:  Yunpeng Zhou - The University of Hong Kong (Hong Kong) [presenting]
KC Yuen - HKU (China)
Abstract: High-dimensional data is commonly observed in survival data analysis. Penalized regression is widely applied for parameter selection given this type of data. The LASSO, SCAD and MCP methods are basic penalties developed in recent years in order to achieve a more accurate selection of parameters. The l0 penalty, which selects the best subset of parameters and provides unbiased estimation, is not fully researched due to its NP-hard complexity resulting from the non-smooth and non-convex objective function. Most methods developed so far focus on providing a smoothed version of the l0-norm which does not address the problem directly. Two Augmented Lagrangian-based algorithms are proposed for the additive hazard model, namely the ADMM-l0 method and the APM-l0 method, to approximate the optimal solution generated by the l0 penalty, among which the ADMM-l0 algorithm can achieve unbiased parameter estimation. Also, under moderate sample sizes, both methods perform well in selecting the best subset of parameters, especially in terms of controlling the false positive rate. The convergence of ADMM-l0 is proved under strict assumptions, and the performance of the proposed methods is illustrated using two DLBCL datasets.