论文标题
支持检测和根系寻找高维广义线性模型的方法
A Support Detection and Root Finding Approach for Learning High-dimensional Generalized Linear Models
论文作者
论文摘要
特征选择对于建模高维数据很重要，其中变量的数量可能比样本量大得多。在本文中，我们开发了一个支持检测和根检测程序，以学习高维稀疏的广义线性模型，并用GSDAR表示此方法。基于$ \ ell_0 $ penalized最大似然估计的KKT条件，GSDAR会在迭代中生成一系列估算器。 在对目标系数上最大似然函数和稀疏性假设上的某些限制性可逆条件下，提出的估计值的误差将指数衰减至最佳顺序。此外，如果目标信号强于可检测水平，则可以恢复甲骨文估计器。 我们进行仿真和实际数据分析，以说明我们提出的方法比包括Lasso和MCP在内的几种现有方法的优势。
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional sparse generalized linear models and denote this method by GSDAR. Based on the KKT condition for $\ell_0$-penalized maximum likelihood estimations, GSDAR generates a sequence of estimators iteratively. Under some restricted invertibility conditions on the maximum likelihood function and sparsity assumption on the target coefficients, the errors of the proposed estimate decays exponentially to the optimal order. Moreover, the oracle estimator can be recovered if the target signal is stronger than the detectable level. We conduct simulations and real data analysis to illustrate the advantages of our proposed method over several existing methods, including Lasso and MCP.
