【摘要】 稀疏logistic回归,是机器学习中一类重要的问题,它在控制论、管理科学和互联网等领域有着广泛的应用.本文提出了一种改进的基于分象限学习的拟Newton算法来求解稀疏logistic回归问题.新算法采用著名的Barzilai-Borwein步长策略自适应地近似代替目标函数的Hesse阵,并利用目标函数的整体梯度信息来构造拟Newton向量.在适当的条件下,证明了新算法的全局收敛性.数值实验表明新算法是可行的,并且是有效的.更多还原

【Abstract】 Sparse logistic regression, is a class of important problems in machine learning, which has wide applications in cybernetics, management sciences and internet, etc. This paper proposes an Improved OrthantWise Limited-memory Quasi-Newton(IOWL-QN) method for sparse logistic regression problems. The proposed method adopts the well-known BB stepsize strategy to approximate the Hessian of the goal objective function, and constructs the quasi-Newton vectors based on the gradient of the goal objective function. Under mild conditions,global convergence of the proposed method is established. Numerical results are reported to illustrate that the proposed method is feasible and efficient.更多还原