Stochastic block models: A comparison of variants and inference methods.

Area of Science:

• Network Science
• Statistical Modeling
• Data Analysis

Background:

• Community detection in complex networks is a significant challenge.
• The Stochastic Block Model (SBM) is a promising approach, but numerous variants and inference methods exist due to interdisciplinary influences.
• A comprehensive comparison of these techniques is necessary to understand their capabilities and limitations.

Purpose of the Study:

• To review and unify the notation of various SBM variants, explaining their developmental rationale.
• To discuss and analyze different methods for inferring optimal partitions within SBMs.
• To provide guidance for selecting SBM variants and inference methods and to offer a heuristic for Metropolis-Hastings algorithm parameter tuning.

Main Methods:

• Review of SBM variants (e.g., degree-corrected SBM, hierarchical SBM).
• Discussion of inference approaches (e.g., Metropolis-Hastings algorithm).
• Analysis using an extended Girvan-Newman test, the Lancichinetti-Fortunato-Radicchi benchmark, and real-world networks.

Main Results:

• A uniform notation for SBM variants and their development reasons are presented.
• Comparative analysis of SBM variants and inference methods on benchmark and real-world networks.
• A heuristic for determining Metropolis-Hastings algorithm steps is proposed.

Conclusions:

• The study offers guidance for researchers in selecting SBM variants and inference methods.
• It highlights limitations in current techniques, aiming to direct future research.
• Freely available code is provided to foster development and idea exchange in the SBM field.