Model-free Bayesian Clustering and Multimodal Posterior Summarisation

Abstract:We develop a model-free, noise-aware Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive Bayesian perspective. This avoids explicit likelihood-prior model specification, expensive MCMC sampling, and mode-seeking variational approximations, while accommodating irregular cluster shapes and enabling parallel generation of posterior draws. To interpret the posterior over high-dimensional, noise-aware clusterings, we introduce a Wasserstein-type summarization method. Using a novel noise-aware loss, this approach compresses the large collection of posterior draws into a small set of weighted representatives, capturing distinct cluster structures and noise assignments. Further, we marginalise the uncertainty in the density level, avoiding reliance on a specific choice. We establish theoretical properties of the proposed loss and guarantees for the level-marginal posterior approximation. Results demonstrate the framework's effectiveness in capturing clustering and noise uncertainty.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.13397 [stat.ML]

(or arXiv:2610.13397v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.13397 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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