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Bootstrap quantification of estimation uncertainties in network degree distributions.

Yulia R Gel1, Vyacheslav Lyubchich2, L Leticia Ramirez Ramirez3

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We introduce a fast patchwork bootstrap (FPB) method for accurate uncertainty quantification in large, ultra-sparse networks. This approach provides better confidence intervals for network degree distributions than existing methods.

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Area of Science:

  • Network Science
  • Statistical Inference
  • Computational Statistics

Background:

  • Quantifying estimation uncertainties in network functions is challenging, especially in large, ultra-sparse networks where degree distributions are unknown.
  • Existing bootstrap methods may not be suitable for the unique structure of ultra-sparse random networks.

Purpose of the Study:

  • To develop a novel nonparametric bootstrap method for quantifying estimation uncertainties in functions of network degree distribution.
  • To address the challenges posed by large, ultra-sparse networks with unknown network order and degree distribution.

Main Methods:

  • Adaptation of the 'blocking' argument from time series and spatial data to random networks, creating 'patches' of ego networks.
  • Development of a computationally efficient, data-driven cross-validation algorithm for optimal patch size selection.
  • The proposed Fast Patchwork Bootstrap (FPB) methodology is applied to network mean degree and degree distribution inference.

Main Results:

  • The FPB method provides sharper and better-calibrated confidence intervals compared to competing approaches.
  • Demonstrated superior performance in simulation studies, particularly for networks in the ultra-sparse regime.
  • FPB is computationally less expensive, requires less graph information, and is free from nuisance parameters.

Conclusions:

  • The Fast Patchwork Bootstrap (FPB) offers a robust and efficient solution for uncertainty quantification in large, ultra-sparse networks.
  • FPB is applicable to various network types, including collaboration and Wikipedia networks, demonstrating its practical utility.