Optimal subsampling for regression with mixed‐type predictors

Subsampling has emerged as an appealing strategy to mitigate the computational and storage challenges imposed by large datasets. Recent subsampling techniques have shown notable computational gains for data dominated by numerical predictors. However, real‐world datasets frequently contain both numerical and categorical predictors. Traditional treatments of categorical predictors commonly use dummy coding, which can lead to substantial dimensional expansion and added complexity during subsampling. To address these challenges, we propose a new mixed‐type optimal subsampling technique (MOST) specifically designed for both numerical and categorical predictors. By enforcing combinatorial orthogonality, MOST effectively captures the informative structure of mixed‐type predictors, enabling more efficient subdata estimators. Simulation studies and real‐data applications demonstrate the superior accuracy and computational benefits of MOST compared to existing subsampling methods.