# Scalable Posterior Uncertainty for Flexible Density-Based Clustering

arXiv: https://arxiv.org/abs/2603.03188 · HTML: https://mlsanity.com/paper/2603.03188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 73 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [A Population Background for Nonparametric Density-Based Clustering](https://mlsanity.com/paper/1408.1381/) (2014)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [Are Gibbs-type priors the most natural generalization of the Dirichlet process?](https://mlsanity.com/paper/1503.00163/) (2015)
- [Search Algorithms and Loss Functions for Bayesian Clustering](https://mlsanity.com/paper/2105.04451/) (2021)
- [Bayesian Repulsive Gaussian Mixture Model](https://mlsanity.com/paper/1703.09061/) (2017)
- [Inconsistency of Pitman-Yor process mixtures for the number of components](https://mlsanity.com/paper/1309.0024/) (2013)
- [Clustering consistency with Dirichlet process mixtures](https://mlsanity.com/paper/2205.12924/) (2022)
- [Scalable Bayesian Nonparametric Clustering and Classification](https://mlsanity.com/paper/1806.02670/) (2018)
- [Bayesian Clustering via Fusing of Localized Densities](https://mlsanity.com/paper/2304.00074/) (2023)
- [Modeling with Normalized Random Measure Mixture Models](https://mlsanity.com/paper/1310.0260/) (2013)
- [Bayesian Quantile Estimation and Regression with Martingale Posteriors](https://mlsanity.com/paper/2406.03358/) (2024)
- [Conformalized Bayesian Inference, with Applications to Random Partition Models](https://mlsanity.com/paper/2511.05746/) (2025)
- [Martingale Posteriors from Score Functions](https://mlsanity.com/paper/2501.01890/) (2025)
- [Repulsive Mixture Model with Projection Determinantal Point Process](https://mlsanity.com/paper/2510.08838/) (2025)
- [Repulsion, Chaos and Equilibrium in Mixture Models](https://mlsanity.com/paper/2306.10669/) (2023)
- [Bayesian Level Set Clustering](https://mlsanity.com/paper/2403.04912/) (2024)

## Built on by (most cited first, 1 of 1)

- [On Bayesian Softmax-Gated Mixture-of-Experts Models](https://mlsanity.com/paper/2604.20551/) (2026)

## Abstract (arXiv)

We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level of a mixture model, we treat clusters as explicit functionals of the data-generating density, without assuming any specific parametric form. To characterize density uncertainty, we obtain martingale posterior samples via a predictive resampling scheme driven by model score evaluations. This allows us to leverage state-of-the-art differentiable density estimators, such as normalizing flows, making density resampling efficient in large-scale settings and fully parallelizable on modern GPU hardware. Martingale posterior samples of the clustering structure are then obtained by applying density-based clustering to the density draws, enabling principled inference on any clustering-related quantity. Casting the inference target as a density functional further enables a rigorous theoretical analysis of the procedure's convergence properties. We apply our methodology to image and single-cell RNA sequencing data, demonstrating the computational efficiency afforded by its GPU compatibility as well as its ability to recover meaningful clustering structures, with associated uncertainty, across diverse domains.