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Summary
This summary is machine-generated.

This study introduces a new detectability threshold for the stochastic block model using the expectation-maximization (EM) algorithm with belief propagation (BP). This threshold accounts for inaccuracies in learning model parameters, differing from the traditional Nishimori condition.

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Area of Science:

  • Statistical Inference
  • Network Science
  • Machine Learning

Background:

  • Detectability analysis of stochastic block models typically assumes known or perfectly learned model parameters (Nishimori condition).
  • In real-world applications, model parameters are often unknown or learned with inaccuracies, challenging existing theoretical frameworks.

Purpose of the Study:

  • To derive the algorithmic detectability threshold for the stochastic block model using the expectation-maximization (EM) algorithm combined with belief propagation (BP).
  • To analyze the detectability of general modular structures, not limited to simple community structures.

Main Methods:

  • Utilized the expectation-maximization (EM) algorithm integrated with belief propagation (BP) for parameter estimation.
  • Derived the theoretical algorithmic detectability threshold based on the performance of the EM-BP algorithm.

Main Results:

  • The study establishes an algorithmic detectability threshold that differs qualitatively from the threshold derived under the Nishimori condition.
  • The derived threshold is applicable to general modular structures within networks.

Conclusions:

  • The findings highlight the practical limitations of the Nishimori condition in real-world network analysis.
  • The developed EM-BP based threshold provides a more realistic measure for detecting structures in stochastic block models when parameters are learned.