Modern Subsampling Methods for Large-Scale Least Squares Regression

Subsampling methods aim to select a subsample as a surrogate for the observed sample. As a powerful technique for large-scale data analysis, various subsampling methods are developed for more effective coefficient estimation and model prediction. This review presents some cutting-edge subsampling methods based on the large-scale least squares estimation. Two major families of subsampling methods are introduced: the randomized subsampling approach and the optimal subsampling approach. The former aims to develop a more effective data-dependent sampling probability while the latter aims to select a deterministic subsample in accordance with certain optimality criteria. Real data examples are provided to compare these methods empirically, respecting both the estimation accuracy and the computing time.