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Model selection for degree-corrected block models.

Xiaoran Yan1, Cosma Shalizi2, Jacob E Jensen3

  • 1Information Sciences Institute, University of Southern California, Marina del Rey, CA 90292, USA.

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Summary
This summary is machine-generated.

Selecting the right network model is crucial for analyzing sparse, high-dimensional data. This study introduces a principled method for choosing between stochastic block models and degree-corrected block models, improving community detection in networks.

Keywords:
clustering techniquesmessage-passing algorithmsnetworksrandom graphsstatistical inference

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Area of Science:

  • Network analysis
  • Statistical modeling
  • Graph theory

Background:

  • Network data presents unique challenges for model selection due to sparsity and global dependencies.
  • Traditional model-selection criteria are often inadequate for high-dimensional network models with latent variables.
  • Community detection in networks is a key problem, often addressed by stochastic block models (SBMs).

Purpose of the Study:

  • To address the challenge of selecting between standard stochastic block models (SBMs) and degree-corrected block models (DCBMs).
  • To develop a principled and computationally tractable method for model selection in network analysis.
  • To improve the accuracy of community detection by choosing the appropriate block model.

Main Methods:

  • Developed new large-graph asymptotic results for the distribution of log-likelihood ratios under SBMs.
  • Introduced linear-time approximations for log-likelihoods using belief propagation for both SBM and DCBM.
  • Applied the new model-selection approach to simulated and real-world network data.

Main Results:

  • Demonstrated substantial departures from classical results for sparse graphs using large-graph asymptotics.
  • Achieved excellent agreement between approximated and exact log-likelihoods in applications.
  • Provided a practical solution for deciding on degree correction in block model selection.

Conclusions:

  • The proposed method offers a reliable approach for model selection between SBM and DCBM, crucial for accurate community detection.
  • The findings highlight the limitations of classical methods for sparse network data and offer improved alternatives.
  • This work establishes a general framework for model selection applicable to various network analysis problems.