Chengyu Ke: Iteratively Reweighted Group LASSO Based on Log-composite Regularization

This paper addresses supervised learning problems with grouping information on model coefficients given a priori. We focus on non-overlapping groups such that coefficients for each disjoint group shall be simultaneously either zero or nonzero. To deal with such group sparsity structure, we introduce a novel log-composite regularizer, which can be minimized by an iterative algorithm. In particular, our algorithm iteratively solves for a traditional group LASSO problem that involves summing up the L2 norm of each group until convergent. By updating group weights, our approach enforces a group of smaller coefficients from the previous iterate to be more likely to set to zero, compared to the group LASSO. Theoretical results include a minimizing property of the proposed model as well as the convergence of the iterative algorithm to a stationary solution under mild conditions. We conduct extensive experiments on synthetic and real datasets, indicating that our method yields superior performance over the state-of-the-art methods in linear regression and binary classification.