Balanced Subsampling for Big Data with Categorical Covariates

Abstract: Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource limitations. Subsampling algorithms offer a solution by selecting a subset from the design points for observing the response. Existing subsampling methods primarily assume numerical predictors, neglecting the prevalent occurrence of big data with categorical predictors across various disciplines. This paper proposes a novel balanced subsampling approach tailored for data with categorical predictors. A balanced subsample significantly reduces the cost of observing the response and possesses three desired merits. First, it is nonsingular and, therefore, allows linear regression with all dummy variables encoded from categorical predictors. Second, it offers optimal parameter estimation by minimizing the generalized variance of the estimated parameters. Third, it allows robust prediction in the sense of minimizing the worst-case prediction error. We demonstrate the superiority of balanced subsampling over existing methods through extensive simulation studies and a real-world application.