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Online inference in high-dimensional generalized linear models with streaming data.

Lan Luo1, Ruijian Han2, Yuanyuan Lin3

  • 1Department of Biostatistics and Epidemiology, Rutgers School of Public Health, New Jersey, USA.

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|August 27, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an online statistical inference method for high-dimensional generalized linear models using streaming data. The novel online debiased lasso efficiently estimates regression coefficients and enables real-time statistical inference.

Keywords:
62F25Confidence intervalPrimary 62J07generalized linear modelshigh-dimensional dataonline debiased lassosecondary 62J12

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional generalized linear models (GLMs) are crucial for analyzing complex datasets.
  • Streaming data requires efficient online methods for real-time estimation and inference.
  • Traditional offline methods are unsuitable for continuous data streams.

Purpose of the Study:

  • To develop an online statistical inference approach for high-dimensional GLMs with streaming data.
  • To enable real-time estimation and inference on continuously arriving data.
  • To address the limitations of offline methods in dynamic data environments.

Main Methods:

  • Proposing an online debiased lasso method tailored for streaming data.
  • Updating confidence intervals using only historical summary statistics.
  • Incorporating an additional term to correct accumulated approximation errors during online updates.

Main Results:

  • The proposed online debiased estimators in GLMs are shown to be asymptotically normal.
  • This asymptotic normality provides theoretical justification for real-time interim inference.
  • Numerical experiments validate the effectiveness and performance of the online debiased lasso method.

Conclusions:

  • The developed online debiased lasso method offers a robust solution for statistical inference with high-dimensional streaming data.
  • The theoretical results support the application of this method for real-time analysis.
  • The approach is demonstrated to be effective, even on large-scale text datasets.