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.
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BibTeX
@misc{li2026modelfree,
title = {{Model-free Bayesian Clustering and Multimodal Posterior Summarisation}},
author = {Qing Li and Sara Wade},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13397},
eprint = {2610.13397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13397},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model-free Bayesian Clustering and Multimodal Posterior Summarisation
AU - Qing Li
AU - Sara Wade
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13397
UR - https://arxiv.org/abs/2610.13397
AB - 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.
ER -