An Extended Newton-type Algorithm for ℓ2-Regularized Sparse Logistic Regression and Its Efficiency for Classifying Large-scale Datasets

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the ℓ1-regularized version to the sparsity constrained models. This paper is carried out on the sparsity constrained logistic regression by the Newton method. We begin with establishing its first-order optimality condition associated with a τ-stationary point. This point can be equivalently interpreted as a system of equations which is then efficiently solved by the Newton method. The method has a considerably low computational complexity and enjoys global and quadratic convergence properties. Numerical experiments on random and real data demonstrate its superior performance when against seven state-of-the-art solvers.