Weighted stochastic block model.

Area of Science:

• Network analysis
• Statistical modeling
• Machine learning

Background:

• Stochastic block models (SBMs) are foundational for network community detection.
• Existing SBMs primarily focus on unweighted networks, limiting their application to weighted network analysis.
• Weighted networks are prevalent in various domains, necessitating models that account for edge weights.

Purpose of the Study:

• To introduce the weighted stochastic block model (WSBM), an extension of SBMs for weighted networks.
• To develop and validate methods for parameter estimation and model selection in WSBMs.
• To demonstrate the utility of WSBMs through simulations and real-world data analysis.

Main Methods:

• Maximum likelihood estimation for WSBM parameter inference.
• Variational inference approaches for scalable WSBM parameter estimation.
• Model selection criteria for determining the optimal number of latent classes in WSBMs.

Main Results:

• The proposed maximum likelihood and variational estimators for WSBMs are shown to be consistent.
• A method for selecting the number of classes in WSBMs is presented and evaluated.
• The WSBM successfully captures community structure in both simulated and real-world weighted network data.

Conclusions:

• The weighted stochastic block model (WSBM) provides a robust framework for analyzing weighted networks.
• The developed estimation and model selection techniques ensure reliable WSBM application.
• WSBM is a valuable tool for uncovering latent structures in complex weighted network data.