Optimal subsampling for large scale Elastic-net regression

The sheer volume of data has been generated from the fields of computer vision, medical imageology, astronomy, web information tracking, etc., which hampers the implementation of various statistical algorithms. An efficient and popular method to reduce the computation burden is subsampling. Previous studies focused on subsampling algorithms for non-regularized regression such as ordinary least square regression and logistic regression. In this article, we introduce a flexible and efficient subsampling algorithm based on A-optimality for Elastic-net regression. Theoretical results are given describing the statistical properties of the proposed algorithm. Four numerical examples are given to examine the promising empirical characteristics of the technique. Finally, the algorithm is applied in Blog and 2D-CT slice datasets in reality and has shown a significant lead over the traditional leveraging subsampling method.