Projection-Uniform Subsampling Methods for Big Data

Yuxin Sun, Wenjun Liu and Ye Tian ()
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Yuxin Sun: Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China
Wenjun Liu: Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China
Ye Tian: Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China

Mathematics, 2024, vol. 12, issue 19, 1-16

Abstract: The idea of experimental design has been widely used in subsampling algorithms to extract a small portion of big data that carries useful information for statistical modeling. Most existing subsampling algorithms of this kind are model-based and designed to achieve the corresponding optimality criteria for the model. However, data generating models are frequently unknown or complicated. Model-free subsampling algorithms are needed for obtaining samples that are robust under model misspecification and complication. This paper introduces two novel algorithms, called the Projection-Uniform Subsampling algorithm and its extension. Both algorithms aim to extract a subset of samples from big data that are space-filling in low-dimensional projections. We show that subdata obtained from our algorithms perform superiorly under the uniform projection criterion and centered L 2 -discrepancy. Comparisons among our algorithms, model-based and model-free methods are conducted through two simulation studies and two real-world case studies. We demonstrate the robustness of our proposed algorithms in building statistical models in scenarios involving model misspecification and complication.

Keywords: model-free subsampling; space-filling design; uniform projection criterion; centered L 2 -discrepancy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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