A robust regularization path for the Doubly Regularized Support Vector Machine

The Doubly Regularized SVM (DrSVM) is an extension of SVM using a mixture of L2 and L1 norm penalties. This kind of penalty, sometimes referred as the elastic net, allows to perform variable selection while taking into account correlations between variables. Introduced by Wang [1], an e cient algorithm to compute the whole DrSVM solution path has been proposed. Unfortunately, in some cases, this path is discontinuous, and thus not piecewise linear. To solve this problem, we propose here a new sub gradient formulation of the DrSVM problem. This led us to propose an alternative L1 regularization path algorithm. This reformulation e ciently addresses the aforementioned problem and makes the initialization step more generic. The results show the validity of our sub-gradient formulation and the e ciency compared to the initial formulation.