We introduce a novel framework for uncertainty quantification in clustering. By combining the martingale posterior paradigm with density-based clustering, uncertainty in the estimated density is naturally propagated to the clustering structure. The approach scales effectively to high-dimensional and irregularly shaped data by leveraging modern neural density estimators and GPU-friendly parallel computation. We establish frequentist consistency guarantees and validate the methodology on synthetic and real data.

翻译：本文提出了一种新颖的聚类不确定性量化框架。通过将鞅后验范式与基于密度的聚类方法相结合，估计密度的不确定性能够自然地传递到聚类结构中。该方法利用现代神经密度估计器与GPU友好的并行计算，可有效扩展至高维及不规则形状的数据处理。我们建立了频率学派的一致性保证，并在合成数据与真实数据上验证了该方法的有效性。