Error Function Regularization: A New Approach to Sparse Logistic Regression

We introduce the ERror Function (ERF) for sparse logistic regression. The ERF regularization interpolates between the L0 norm, which measures the number of non-zero elements in a vector, and its convex relaxation, the L1 norm, controlled by a hyper-parameter. Building on an Iterative Reweighted L1 (IRL1) scheme and the Alternating Direction Method of Multipliers (ADMM), we develop an effective algorithm to minimize the proposed model and analyze its convergence. Experiments on both synthetic and real high-dimensional datasets demonstrate the empirical competitiveness of our approach.