Supervised compression of big data

The phenomenon of big data has become ubiquitous in nearly all disciplines, from science to engineering. A key challenge is the use of such data for fitting statistical and machine learning models, which can incur high computational and storage costs. One solution is to perform model fitting on a carefully selected subset of the data. Various data reduction methods have been proposed in the literature, ranging from random subsampling to optimal experimental design‐based methods. However, when the goal is to learn the underlying input–output relationship, such reduction methods may not be ideal, since it does not make use of information contained in the output. To this end, we propose a supervised data compression method called supercompress, which integrates output information by sampling data from regions most important for modeling the desired input–output relationship. An advantage of supercompress is that it is nonparametric—the compression method does not rely on parametric modeling assumptions between inputs and output. As a result, the proposed method is robust to a wide range of modeling choices. We demonstrate the usefulness of supercompress over existing data reduction methods, in both simulations and a taxicab predictive modeling application.