稀疏逻辑回归问题的一个光滑化共辄梯度算法

A Smoothing Conjugate Gradient Algorithm for Sparse Logistic Regression Problems

稀疏逻辑回归是一种具有稀疏约束的逻辑回归模型,它广泛应用于神经网络、 机器学习和生物信 息领域。 本文基于近似l1-范数的思想,采用六个光滑函数对稀疏逻辑回归模型中的l1- 范数的每个 分量进行近似,将问题转换为光滑化无约束最小化问题,然后设计共辄梯度法求解近似模型井给 出收敛性分析。 最后通过数值实验与己知求解稀疏逻辑回归模型的四个算法进行比较,得出共辄 梯度法求解稀疏逻辑回归问题是有效的。

Sparse logistic regression is a kind of logistic regression model with sparse constraints, which is widely used in the fields of neural networks, machine learning, and bioinfor- matics. In this paper, based on the idea of approximating the l1 norm, six smooth functions are used to approximate each component of the l1 norm in the sparse logis- tic regression model, and the problem is transformed into a smoothed unconstrained minimization problem, then a conjugate gradient method is designed to solve the approximated model and the convergence analysis is given. Finally, numerical exper- iments are conducted to compare with four known algorithms for solving the sparse logistic regression model, and it is concluded that the conjugate gradient method is effective in solving the sparse logistic regression problem.