L1-2 Regularized Logistic Regression

Logistic regression has become a fundamental tool to facilitate data analysis and prediction in a variety of applications, including health care and social sciences. Depending on different sparsity assumptions, logistic regression models often incorporate various regularizations, including l(1)-norm, l(2)-norm and some non-convex regularizations. In this paper, we propose a non-convex l(1)-regularized logistic regression model assuming that the coefficients to be recovered are highly sparse. We derive two numerical algorithms with guaranteed convergence based on the alternating direction method of multipliers and the proximal operator of l(1-2). Numerical experiments on real data demonstrate the great potential of the proposed approach.