An efficient subsampling algorithm for big data with interaction effects under measurement constraints

Abstract

The rapid growth of big data sets has made subsampling an essential tool for data storage and analysis. In many applications, first‐order models are inadequate, as interaction and quadratic effects are often present. Second‐order models provide a concise framework for capturing such higher‐order relationships, yet subsampling strategies tailored to these models remain underexplored. Hence, we propose an efficient subsampling method for second‐order models (ESSO) inspired by orthogonal arrays. Our method is particularly suited for scenarios with measurement constraints, where subsample selection does not require response information. This study examines the optimal subsampling method under the ‐optimality criterion for second‐order models. Additionally, the asymptotic normality of the estimator is established, and a sequential algorithm is proposed for practical implementation. Numerical simulations and a real data example further demonstrate the effectiveness of the proposed approach.