Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic regression with nonconvex regularization term. In this paper, we propose a unified framework to solve $\ell_1$-regularized logistic regression, which can be naturally extended to nonconvex regularization term, as long as certain requirement is satisfied. In addition, we also utilize a different line search criteria to guarantee monotone convergence for various 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 at a lower computational cost.

翻译：稀疏逻辑回归同时用于分类和特征选择。尽管已有大量研究致力于求解$\ell_1$正则化逻辑回归问题，但在非凸正则化项下的稀疏逻辑回归求解工作相对较少。本文提出一个统一框架以求解$\ell_1$正则化逻辑回归，该框架在满足特定条件时可自然扩展至非凸正则化项。此外，我们采用不同的线性搜索准则保证多种正则化项下的单调收敛性。基于真实数据集的二分类任务实验表明，所提出的算法能以较低计算成本有效完成分类与特征选择。