Sparse logistic regression aims to perform classification and feature selection simultaneously for high-dimensional data. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant literature about solving sparse logistic regression associated with nonconvex penalties. In this paper, we propose to solve $\ell_1$-regularized sparse logistic regression and some nonconvex penalties-regularized sparse logistic regression, when the nonconvex penalties satisfy some prerequisites, with similar optimization frameworks. In the proposed optimization frameworks, we utilize different line search criteria to guarantee good convergence performance for different regularization terms. Empirical experiments on binary classification tasks with real-world datasets demonstrate our proposed algorithms are capable of performing classification and feature selection effectively with a lower computational cost.

翻译：稀疏逻辑回归旨在对高维数据同时进行分类和特征选择。尽管已有大量研究解决$\ell_1$正则化逻辑回归问题，但关于结合非凸惩罚项的稀疏逻辑回归求解方法的研究相对较少。本文针对满足特定前提条件的非凸惩罚项，提出采用相似优化框架求解$\ell_1$正则化稀疏逻辑回归及若干非凸惩罚项正则化稀疏逻辑回归问题。在所提优化框架中，我们利用不同的线搜索准则确保各正则化项具有良好的收敛性能。基于真实数据集的二分类任务实验表明，所提算法能以较低计算成本有效实现分类与特征选择。