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Stochastic DCA for the Large-sum of Non-convex Functions Problem and its Application to Group Variable Selection in Classification
Hoai An Le Thi · Hoai Minh Le · Duy Nhat Phan · Bach Tran

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #60
In this paper, we present a stochastic version of DCA (Difference of Convex functions Algorithm) to solve a class of optimization problems whose objective function is a large sum of non-convex functions and a regularization term. We consider the $\ell_{2,0}$ regularization to deal with the group variables selection. By exploiting the special structure of the problem, we propose an efficient DC decomposition for which the corresponding stochastic DCA scheme is very inexpensive: it only requires the projection of points onto balls that is explicitly computed. As an application, we applied our algorithm for the group variables selection in multiclass logistic regression. Numerical experiments on several benchmark datasets and synthetic datasets illustrate the efficiency of our algorithm and its superiority over well-known methods, with respect to classification accuracy, sparsity of solution as well as running time.

Author Information

Hoai An Le Thi (Theoretical and Applied Computer Science Laboratory, University of Lorraine)
Hoai Minh Le (Laboratory of Theoretical and Applied Computer Science, Univ. of Lorraine, Fr)
Duy Nhat Phan (Universite de Lorraine)
Bach Tran (University of Lorraine)

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