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Entropy of stochastic blockmodel ensembles.
1Institut für Theoretische Physik, Universität Bremen, Germany. tiago@itp.uni-bremen.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study derives entropy expressions for stochastic blockmodels, including degree-corrected variants. This enables better inference of network community structures, even with complex degree correlations.
Area of Science:
- Network science
- Statistical modeling
- Information theory
Background:
- Stochastic blockmodels (SBMs) are fundamental generative models for network analysis.
- Existing SBMs often struggle with networks exhibiting degree heterogeneity or correlations.
- Entropy is a key measure for characterizing statistical ensembles and model uncertainty.
Purpose of the Study:
- To derive and analyze the entropy of various stochastic blockmodel ensembles.
- To extend SBM entropy calculations to degree-corrected, multigraph, and directed graph models.
- To demonstrate the utility of entropy expressions for inferring latent network structure.
Main Methods:
- Derivation of analytical expressions for the entropy of SBM ensembles.
- Consideration of traditional SBMs and degree-corrected SBMs with soft and hard constraints.
- Generalization of methods to multigraphs and directed graphs.
- Direct derivation of a log-likelihood function from entropy for model inference.
Main Results:
- Novel entropy expressions for diverse SBM variants are presented.
- The derived entropy provides a principled way to infer latent block structure.
- The method effectively handles both intrinsic and extrinsic degree correlations in networks.
- Applications include direct log-likelihood function derivation for network inference.
Conclusions:
- The derived entropy expressions offer a powerful tool for understanding and applying stochastic blockmodels.
- The framework accommodates complex network features like degree correlations.
- This work advances the statistical foundations of network community detection and generative modeling.
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