# An Extended Newton-type Algorithm for $\ell_2$-Regularized Sparse Logistic Regression and Its Efficiency for Classifying Large-scale Datasets

## TL;DR

This paper introduces an extended Newton-type algorithm for $ ext{l}_2$-regularized sparse logistic regression, demonstrating its efficiency and superior performance on large-scale datasets compared to existing solvers.

## Contribution

It develops a novel Newton-based method for sparsity constrained logistic regression with proven convergence properties and improved computational efficiency.

## Key findings

- Achieves global and quadratic convergence.
- Outperforms seven state-of-the-art solvers in experiments.
- Efficiently handles large-scale datasets.

## Abstract

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-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 $\tau$-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.