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Robust and efficient subsampling algorithms for massive data logistic regression.

Jun Jin1, Shuangzhe Liu2, Tiefeng Ma3

  • 1College of Mathematical Sciences, Yangzhou University, Yangzhou, People's Republic of China.

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|June 12, 2024
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Summary
This summary is machine-generated.

New algorithms address computational limits in massive data analysis. These methods improve logistic regression estimation by using a hard threshold or combining subsamples, enhancing efficiency for large datasets.

Keywords:
Massive dataasymptotic distributionlogistic regressionoptimal subsampling

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Area of Science:

  • Statistics
  • Computer Science
  • Data Science

Background:

  • Massive datasets (big data) present computational challenges for analysis.
  • Nonuniform subsampling reduces computational load but can increase estimator variance with heterogeneous probabilities.
  • Existing methods struggle with the scale and complexity of modern data.

Purpose of the Study:

  • To develop novel algorithms for improved logistic regression estimation in massive datasets.
  • To address the limitations of existing nonuniform subsampling methods.
  • To enhance computational efficiency and statistical inference for big data.

Main Methods:

  • A hard threshold algorithm is proposed, replacing low subsampling probabilities with a chosen threshold.
  • A combining subsamples method is introduced, aggregating estimates from multiple subsamples.
  • Asymptotic properties of the proposed estimators are theoretically established.

Main Results:

  • The hard threshold method offers a way to manage subsampling probabilities.
  • The combining subsamples method improves estimation efficiency without needing a sandwich matrix.
  • Simulations and real-world data analysis demonstrate the practical effectiveness of both methods.

Conclusions:

  • The developed algorithms provide effective solutions for logistic regression with massive data.
  • These methods enhance computational efficiency and statistical accuracy.
  • The findings offer practical tools for analyzing large-scale, complex datasets.