University of Michigan - Ann Arbor

In late 2014, it was proven that the elastic net can be reduced to the linear support vector machine.A similar reduction was previously proven for the LASSO in 2014. The authors showed that for every instance of the elastic net, an artificial binary classification problem can be constructed such that the hyper-plane solution of a linear support vector machine (SVM) is identical to the solution {\displaystyle \beta }\beta  (after re-scaling). The reduction immediately enables the use of highly optimized SVM solvers for elastic net problems. It also enables the use of GPU acceleration, which is often already used for large-scale SVM solvers. The reduction is a simple transformation of the original data and regularization constants into new artificial data instances and a regularization constant that specify a binary classification problem and the SVM regularization constant. 
Here,  y 2 consists of binary labels -1,1 . When 2p>n it is typically faster to solve the linear SVM in the primal, whereas otherwise the dual formulation is faster. The authors referred to the transformation as Support Vector Elastic Net (SVEN),

Reduction to support vector machine

 Zhou, Quan; Chen, Wenlin; Song, Shiji; Gardner, Jacob; Weinberger, Kilian; Chen, Yixin. A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing. Association for the Advancement of Artificial Intelligence.(https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/view/9856)

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