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This paper introduces a model-free Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive viewpoint, bypassing explicit model specification and traditional sampling methods. The approach accommodates irregular cluster shapes and enables parallel posterior generation, with a novel Wasserstein-type summarization method used to interpret high-dimensional, noise-aware clusterings by compressing posterior draws into weighted representatives. Theoretical properties of the proposed noise-aware loss and guarantees for level-marginal posterior approximation are established, demonstrating effectiveness in capturing clustering and noise uncertainty.
A model-free Bayesian clustering framework generates a martingale posterior over clusterings without explicit likelihoods or MCMC, effectively handling irregular shapes and noise.
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.
