In a new arXiv preprint, Nicola Bariletto and Stephen G. Walker address a long-standing gap in density-based clustering: the framework is flexible and effective on large, complex datasets, but it has lacked scalable uncertainty quantification. Their method combines density-based clustering with martingale posterior distributions. First, density uncertainty is generated through a fully parallelized predictive resampling scheme driven by model score functions, which naturally accommodates modern differentiable density estimators such as normalizing flows. Each sampled density is then clustered, producing posterior samples of the clustering itself and enabling inference on any clustering-related quantity.
Because the target is treated as a density functional, the authors are also able to provide a rigorous frequentist convergence analysis. They illustrate the approach on image data and single-cell RNA sequencing data, where it recovers meaningful clustering structures, assigns previously unseen data, and yields biologically interpretable cell groupings. The computations run in minutes on a single GPU.
The paper is available on arXiv as 2603.03188.