Optimal Subsampling for Data Streams with Measurement Constrained Categorical Responses

High-velocity, large-scale data streams have become pervasive. Frequently, the associated labels for such data prove costly to measure and are not always available upfront. Consequently, the analysis of such data poses a significant challenge. In this article, we develop a method that addresses this challenge by employing an online subsampling procedure and a multinomial logistic model for efficient analysis of high-velocity, large-scale data streams. Our algorithm is designed to sequentially update parameter estimation based on the A-optimality criterion. Moreover, it significantly increases computational efficiency while imposing minimal storage requirements. Theoretical properties are rigorously established to quantify the asymptotic behavior of the estimator. The method’s efficacy is further demonstrated through comprehensive numerical studies on both simulated and real-world datasets. Supplementary materials for this article are available online.