Technology Category
Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical ModelsData Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
Partially exchangeable stochastic block models for (node-colored) multilayer networks
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
Modeling node-colored multilayer networks with block-connectivity structures
Incorporating layer information via probabilistic construction
Learning node group allocation without compromising coherence
Innovation
Methods, ideas, or system contributions that make the work stand out.
Partially exchangeable stochastic block models
Hierarchical random partition prior
Collapsed Gibbs sampler for inference
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