ABSTRACT

In this paper, a family of coordinate majorization descent algorithms are proposed for solving the nonconvex penalized learning problems including SCAD and MCP estimation. In the coordinate majorization descent algorithms, each coordinate descent step is replaced with a coordinate-wise majorization descent operation, and the convergence of the algorithms are discussed in linear models. In addition, we apply the algorithms to the Logisitic models. Our simulation study and data examples indicate that the coordinate majorization descent algorithms can select the real model with a higher probability and the model is sparse, also the algorithms improve the accuracy of the parameter estimation with SCAD and MCP penalties.

摘要

在本文中，提出了一系列坐标专业化下降算法来解决非凸惩罚学习问题，包括 SCAD 和 MCP 估计。在坐标专业化下降算法中，每个坐标下降步骤都被一个坐标专业化下降操作所代替，并且算法的收敛性在线性模型中进行了讨论。此外，我们将算法应用于 Logisitic 模型。我们的仿真研究和数据实例表明，坐标优先下降算法能够以更高的概率选择真实模型并且模型是稀疏的，并且该算法通过SCAD和MCP惩罚提高了参数估计的准确性。