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Optimized Tail Bounds for Random Matrix Series.

Xianjie Gao1, Mingliang Zhang2, Jinming Luo3

  • 1Department of Basic Sciences, Shanxi Agricultural University, Jinzhong 030801, China.

Entropy (Basel, Switzerland)
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces improved tail bounds for random matrix series, utilizing intrinsic dimensions for better applicability in high-dimensional settings. These new bounds enhance the analysis of matrix Gaussian, sub-Gaussian, and infinitely divisible series.

Keywords:
expectation boundintrinsic dimensionrandom matrix seriestail bound

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Area of Science:

  • Probability and Statistics
  • Mathematical Physics

Background:

  • Random matrix series are crucial in random matrix theory with diverse applications.
  • Existing tail bound analyses often rely on ambient dimension, limiting their scope.

Purpose of the Study:

  • To develop modified tail bounds for random matrix series.
  • To establish bounds based on intrinsic dimension for broader applicability.

Main Methods:

  • Proposed modified tail bounds for matrix Gaussian (or Rademacher), sub-Gaussian, and infinitely divisible (i.d.) series.
  • Derived expectation bounds for random matrix series.

Main Results:

  • New tail bounds are dependent on the intrinsic dimension, not the ambient dimension.
  • The intrinsic dimension-based bounds are effective in high- or infinite-dimensional scenarios.
  • Expectation bounds for random matrix series were successfully obtained using intrinsic dimension.

Conclusions:

  • The modified tail bounds offer improved performance in high-dimensional settings.
  • The intrinsic dimension provides a more refined measure for analyzing random matrix series.
  • This work advances the theoretical understanding and practical application of random matrix series.