Improving optimal subsampling through stratification

2025-12-23

AI Summary

To address two key challenges in large-scale logistic regression—low computational efficiency and difficulties in validation study design under measurement error—this paper proposes an optimal stratified subsampling method. Theoretically, within an asymptotic framework, optimal stratified sampling strictly dominates optimal individualized sampling by eliminating inter-stratum variance contributions, thereby achieving lower estimation variance—a result that breaks the prevailing paradigm benchmarked solely on individualized sampling. We establish a systematic comparative framework between stratified random sampling and individualized probability sampling. Extensive Monte Carlo simulations and empirical analysis using the Vanderbilt CCC real-world clinical cohort consistently demonstrate that the optimal stratified design is not merely a suboptimal approximation to individualized sampling, but possesses intrinsic statistical advantages, significantly improving both computational efficiency and estimation accuracy.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories: (i) designs that optimize individualized sampling rules, where unit-specific probabilities are assigned and applied independently, and (ii) designs based on stratified sampling with simple random sampling within strata. Focusing on the logistic regression setting, we derive the asymptotic variances of estimators under both approaches and compare them numerically through extensive simulations and an application to data from the Vanderbilt Comprehensive Care Clinic cohort. Our results reinforce that stratified sampling is not merely an approximation to individualized sampling, showing instead that optimal stratified designs are often more efficient than optimal individualized designs through their elimination of between-stratum contributions to variance. These findings suggest that optimizing over the class of individualized sampling rules overlooks highly efficient sampling designs and highlight the often underappreciated advantages of stratified sampling.

Problem

• Compares stratified and individualized sampling efficiency in logistic regression.
• Demonstrates optimal stratified designs often reduce variance more effectively.
• Highlights overlooked advantages of stratified over individualized sampling rules.

Innovation

• Stratified sampling optimizes subsampling by eliminating between-stratum variance
• Optimal stratified designs outperform individualized sampling in logistic regression
• Stratification enhances efficiency over individualized probability-based approaches