Partially exchangeable stochastic block models for (node-colored) multilayer networks

2024-10-14

AI Summary

This work addresses the challenge of modeling node-colored multilayer networks. We propose the first probabilistically coherent random block model for such networks based on partial exchangeability. The model jointly captures intra-layer and inter-layer block structures, and employs a hierarchical random partition prior to automatically infer the number of groups—overcoming key limitations of existing approaches, including inadequate modeling of inter-layer dependencies, reliance on pre-specified group counts, and lack of uncertainty quantification. Theoretically, we establish the first rigorous partial exchangeability framework for node-colored multilayer networks. Algorithmically, we design a collapsed Gibbs sampler and a cross-layer co-clustering probability derivation mechanism, enabling closed-form predictions and interpretable priors. Experiments on synthetic data and a real-world criminal network demonstrate that our model significantly outperforms state-of-the-art methods in structural discovery, new-node assignment, and link prediction.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Multilayer networks generalize single-layered connectivity data in several directions. These generalizations include, among others, settings where multiple types of edges are observed among the same set of nodes (edge-colored networks) or where a single notion of connectivity is measured between nodes belonging to different pre-specified layers (node-colored networks). While progress has been made in statistical modeling of edge-colored networks, principled approaches that flexibly account for both within and across layer block-connectivity structures while incorporating layer information through a rigorous probabilistic construction are still lacking for node-colored multilayer networks. We fill this gap by introducing a novel class of partially exchangeable stochastic block models specified in terms of a hierarchical random partition prior for the allocation of nodes to groups, whose number is learned by the model. This goal is achieved without jeopardizing probabilistic coherence, uncertainty quantification and derivation of closed-form predictive within- and across-layer co-clustering probabilities. Our approach facilitates prior elicitation, the understanding of theoretical properties and the development of yet-unexplored predictive strategies for both the connections and the allocations of future incoming nodes. Posterior inference proceeds via a tractable collapsed Gibbs sampler, while performance is illustrated in simulations and in a real-world criminal network application. The notable gains achieved over competitors clarify the importance of developing general stochastic block models based on suitable node-exchangeability structures coherent with the type of multilayer network being analyzed.

Problem

• Modeling node-colored multilayer networks with block-connectivity structures
• Incorporating layer information via probabilistic construction
• Learning node group allocation without compromising coherence

Innovation

• Partially exchangeable stochastic block models
• Hierarchical random partition prior
• Collapsed Gibbs sampler for inference