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
Abstract
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.
BibTeX
@InProceedings{pmlr-v70-thi17a,
title = {Stochastic {DCA} for the Large-sum of Non-convex Functions Problem and its Application to Group Variable Selection in Classification},
author = {Hoai An Le Thi and Hoai Minh Le and Duy Nhat Phan and Bach Tran},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {3394--3403},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/thi17a/thi17a.pdf},
url = {https://proceedings.mlr.press/v70/thi17a.html},
abstract = {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.}
}