A new subspace-based algorithm for efficient spatially adaptive sparse grid regression, classification and multi-evaluation

Abstract

As data has become easier to collect and precise sensors have become ubiquitous, data mining with large data sets has become an important problem. Because sparse grid data mining scales only linearly in the number of data points, large data mining problems have been successfully addressed with this method. Still, highly efficient algorithms are required to process very large problems within a reasonable amount of time. In this paper, we introduce a new algorithm that can be used to solve regression and classification problems on spatially adaptive sparse grids. Additionally, our approach can be used to efficiently evaluate a spatially adaptive sparse grid function at multiple points in the domain. In contrast to other algorithms for these applications, our algorithm fits well to modern hardware and performs only few unnecessary basis function evaluations. We evaluated our algorithm by comparing it to a highly efficient implementation of a streaming algorithm for sparse grid regression. In our experiments, we observed speedups of up to 7×, being faster in all experiments that we performed.