Understanding uncertainty in Bayesian cluster analysis

2025-06-19

AI Summary

In Bayesian clustering, the posterior distribution over partitions is often multimodal or structurally ambiguous, rendering conventional single-point cluster estimates inadequate for characterizing uncertainty. To address this, we propose WASABI (Wasserstein-based Aggregation of Samples for Ambiguous Bayesian Inference), the first method to embed the partition space with the Wasserstein distance—customized for set-based clusterings—and employ a k-medoids–style optimization to extract multiple representative clustering solutions from posterior samples. WASABI explicitly models and interprets multimodal uncertainty without relying on point estimation. It enables accurate quantification of uncertainty in challenging settings, including weakly separated clusters and model misspecification. Experiments on synthetic and real-world datasets demonstrate that WASABI substantially improves the credibility, interpretability, and robustness of clustering results compared to standard approaches.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

The Bayesian approach to clustering is often appreciated for its ability to provide uncertainty in the partition structure. However, summarizing the posterior distribution over the clustering structure can be challenging, due the discrete, unordered nature and massive dimension of the space. While recent advancements provide a single clustering estimate to represent the posterior, this ignores uncertainty and may even be unrepresentative in instances where the posterior is multimodal. To enhance our understanding of uncertainty, we propose a WASserstein Approximation for Bayesian clusterIng (WASABI), which summarizes the posterior samples with not one, but multiple clustering estimates, each corresponding to a different part of the space of partitions that receives substantial posterior mass. Specifically, we find such clustering estimates by approximating the posterior distribution in a Wasserstein distance sense, equipped with a suitable metric on the partition space. An interesting byproduct is that a locally optimal solution to this problem can be found using a k-medoids-like algorithm on the partition space to divide the posterior samples into different groups, each represented by one of the clustering estimates. Using both synthetic and real datasets, we show that our proposal helps to improve the understanding of uncertainty, particularly when the data clusters are not well separated or when the employed model is misspecified.

Problem

• Summarizing Bayesian clustering posterior distribution challenges
• Addressing uncertainty in multimodal clustering partition spaces
• Improving cluster analysis for poorly separated or misspecified data

Innovation

• Wasserstein Approximation for Bayesian clusterIng (WASABI)
• Multiple clustering estimates represent posterior
• k-medoids-like algorithm on partition space