Parallel regressions for variable selection using GPU

Abstract

This paper proposes a parallel regression formulation to reduce the computational time of variable selection algorithms. The proposed strategy can be used for several forward algorithms in order to select uncorrelated variables that contribute for a better predictive capability of the model. Our demonstration of the proposed method include the use of Successive Projections Algorithm (SPA), which is an iterative forward technique that minimizes multicollinearity. SPA is traditionally used for variable selection in the context of multivariate calibration. Nevertheless, due to the need of calculating an inverse matrix for each insertion of a new variable in the model calibration, the computational performance of the algorithm may become impractical as the matrix size increases. Based on such limitation, this paper proposes a new strategy called Parallel Regressions (PR). PR strategy was implemented in the SPA to avoid the matrix inverse calculation of original SPA in order to increase the computational performance of the algorithm. It uses a parallel computing platform called Compute Unified Device Architecture (CUDA) in order to exploit a Graphics Processing Unit, and was called SPA-PR-CUDA. For this purpose, we used a case study involving a large data set of spectral variables. The results obtained with SPA-PR-CUDA presented 37$\times$ times better performance compared to a traditional SPA implementation. Additionally, when compared to traditional algorithms we demonstrated that SPA-PR-CUDA may be a more viable choice for obtaining a model with a reduced prediction error value.