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Projection-Uniform Subsampling Methods for Big Data

Author

Listed:
  • Yuxin Sun

    (Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Wenjun Liu

    (Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Ye Tian

    (Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China
    School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

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.

Suggested Citation

  • Yuxin Sun & Wenjun Liu & Ye Tian, 2024. "Projection-Uniform Subsampling Methods for Big Data," Mathematics, MDPI, vol. 12(19), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:2985-:d:1485701
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    References listed on IDEAS

    as
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