LARS-type algorithm for group lasso

The least absolute shrinkage and selection operator (lasso) has been widely used in regression analysis. Based on the piecewise linear property of the solution path, least angle regression provides an efficient algorithm for computing the solution paths of lasso. Group lasso is an important generalization of lasso that can be applied to regression with grouped variables. However, the solution path of group lasso is not piecewise linear and hence cannot be obtained by least angle regression. By transforming the problem into a system of differential equations, we develop an algorithm for efficient computation of group lasso solution paths. Simulation studies are conducted for comparing the proposed algorithm to the best existing algorithm: the groupwise-majorization-descent algorithm.