A gradient-based optimization algorithm for LASSO

LASSO is a useful method for achieving both shrinkage and variable selection simultaneously. The main idea of LASSO is to use the L1 constraint in the regularization step which has been applied to various models such as wavelets, kernel machines, smoothing splines, and multiclass logistic models. We call such models with the L1 constraint generalized LASSO models. In this paper, we propose a new algorithm called the gradient LASSO algorithm for generalized LASSO. The gradient LASSO algorithm is computationally more stable than QP based algorithms because it does not require matrix inversions, and thus it can be more easily applied to high dimensional data. Simulation results show that the proposed algorithm is fast enough for practical purposes and provides reliable results. To illustrate its computing power with high dimensional data, we analyze multiclass microarray data using the proposed algorithm.