Exchangeable random permutations with an application to Bayesian graph matching

2026-02-02

AI Summary

This work addresses the lack of a flexible and interpretable probabilistic framework for graph matching, particularly in handling uncertainty in node permutations. The authors propose a Bayesian approach based on exchangeable random permutations, linking latent node partitions through the cycle structure of permutations and integrating a stochastic block model for inference. Innovatively, they introduce a position-aware generalized Chinese restaurant process to construct a permutation prior and extend the SALSO algorithm to the permutation domain (perSALSO) for effective posterior uncertainty quantification. By unifying cycle representations, exchangeable partition theory, and block Gibbs sampling over nodes, the method achieves both theoretical rigor and computationally efficient inference of the permutation posterior, enabling practical uncertainty quantification in graph matching tasks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define, characterize, and study the structural and predictive properties of these probabilistic objects. A novel sequential metaphor, the position-aware generalized Chinese restaurant process, provides a constructive foundation for this theory and supports practical algorithmic design. Exchangeable random permutations offer flexible priors for a wide range of inferential problems centered on permutations. As an application, we develop a Bayesian model for graph matching that integrates a correlated stochastic block model with our novel class of priors. The cycle structure of the matching is linked to latent node partitions that explain connectivity patterns, an assumption consistent with the homogeneity requirement underlying the graph matching task itself. Posterior inference is performed through a node-wise blocked Gibbs sampler directly enabled by the proposed sequential construction. To summarize posterior uncertainty, we introduce perSALSO, an adaptation of SALSO to the permutation domain that provides principled point estimation and interpretable posterior summaries. Together, these contributions establish a unified probabilistic framework for modeling, inference, and uncertainty quantification over permutations.

Problem

• graph matching
• permutations
• Bayesian inference
• exchangeability
• uncertainty quantification

Innovation

• exchangeable random permutations
• graph matching
• Chinese restaurant process
• Bayesian inference
• cycle structure