Model-Free Subsampling Method Based on Uniform Designs
Mei Zhang, Yongdao Zhou, Zheng Zhou, Aijun Zhang
Abstract
Subsampling or subdata selection is a useful approach in large-scale statistical learning. Most existing studies focus on model-based subsampling methods which significantly depend on the model assumption. In this article, we consider the model-free subsampling strategy for generating subdata from the original full data. In order to measure the goodness of representation of a subdata with respect to the original data, we propose a criterion, generalized empirical <inline-formula><tex-math notation="LaTeX">$F$</tex-math></inline-formula> -discrepancy (GEFD), and study its theoretical properties in connection with the classical generalized <inline-formula><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -discrepancy in the theory of uniform designs. These properties allow us to develop a kind of low-GEFD data-driven subsampling method based on the existing uniform designs. By simulation examples and a real case study, we show that the proposed subsampling method is superior to the random sampling method. Moreover, our method keeps robust under diverse model specifications while other popular model-based subsampling methods are under-performing. In practice, such a model-free property is more appealing than the model-based subsampling methods, where the latter may have poor performance when the model is misspecified, as demonstrated in our simulation studies. In addition, our method is orders of magnitude faster than other model-free subsampling methods, which makes it more applicable for subsampling of Big Data.