$\ell_1$ regularization has been used for logistic regression to circumvent the overfitting and use the estimated sparse coefficient for feature selection. However, the challenge of such a regularization is that the $\ell_1$ norm is not differentiable, making the standard algorithms for convex optimization not applicable to this problem. This paper presents a simple projection neural network for $\ell_1$-regularized logistics regression. In contrast to many available solvers in the literature, the proposed neural network does not require any extra auxiliary variable nor any smooth approximation, and its complexity is almost identical to that of the gradient descent for logistic regression without $\ell_1$ regularization, thanks to the projection operator. We also investigate the convergence of the proposed neural network by using the Lyapunov theory and show that it converges to a solution of the problem with any arbitrary initial value. The proposed neural solution significantly outperforms state-of-the-art methods with respect to the execution time and is competitive in terms of accuracy and AUROC.
翻译:美元=1美元 正规化用于后勤回归,以绕过超配并使用估计的稀释系数进行特征选择。然而,这种正规化的挑战在于,美元=1美元的规范是无法区分的,因此,对康韦克斯优化的标准算法不适用于这一问题。本文件为1美元=1美元的正规化物流回归提供了一个简单的预测神经网络。与文献中的许多现有解决方案相比,拟议的神经网络并不要求任何额外的辅助变量或任何平稳近似,其复杂性与由于投影操作者而导致的无$=1美元的物流回归梯度的复杂程度几乎相同。我们还利用Lyapunov理论调查拟议的神经网络的趋同,并表明它与任何任意初始价值的这一问题的解决方案相趋同。拟议的神经解决方案大大超出了执行时间方面的最新方法,在准确性和AUROC方面具有竞争力。