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 frequen-tist consistency guarantees and validate the methodology on synthetic and real data.

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world problems. Scalable solutions often rely on classical techniques, such as dropout, during inference or training ensembles of identical models with different random seeds to obtain a posterior distribution. In this paper, we show that these approaches fail to approximate the classification probability. On the contrary, we propose a scalable and intuitive framework to calibrate ensembles of deep learning models to produce uncertainty quantification measurements that approximate the classification probability. On unseen test data, we demonstrate improved calibration, sensitivity (in two out of three cases) and precision when being compared with the standard approaches. We further motivate the usage of our method in active learning, creating pseudo-labels to learn from unlabeled images and human-machine collaboration.