An Efficient Proximal Dc Approach For Fitting The Sparse Envelope Model

The era of big data brings us not only massive data,but also the increase in data complexity and dimension diversity.In data science and statistical learning,to design efficient algorithms for complex multi-dimensional problems has become an important research direction,and it is important to reduce dimension of massive data.The sparse Envelope model is one of the effective models for parameter estimation and response variable selection for high-dimensional data.However,compared with the nice statistical properties that have been established for the sparse Envelope model,the study of the algorithmic issues is not well-developed.In fact,the computational efficiency of solving the non-smooth and non-convex optimization problem arising from the sparse Envelope model is crucial to the applicability of the sparse Envelope model,since such a problem should be solved for many times for cross validation,even for only a single instance.Based on the idea of the DC(Difference of Convex functions)programming and the proximal point method,we propose an accelerated proximal gradient algorithm for the sparse Envelope mod-el.We perform the relaxation of the sparse Envelope model under the framework of DC programming,and we prove the convexity of the relaxation problem.Using the idea of the proximal point algorithm,we propose an accelerated proximal gradient algorithm in order to improve the efficiency of subproblem.Numerical experiments show that the proposed algorithm can greatly reduce the calculation time,compared with the existing block coordinate descent algorithm.