# Distributional Determinantal Point Process for Repulsive Clustering of Distributions

arXiv: https://arxiv.org/abs/2607.21847 · HTML: https://mlsanity.com/paper/2607.21847/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Repulsive Mixture Model with Projection Determinantal Point Process](https://mlsanity.com/paper/2510.08838/) (2025)
- [When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating](https://mlsanity.com/paper/2602.01573/) (2026)
- [Bayesian repulsive mixture model for multivariate functional data](https://mlsanity.com/paper/2603.07320/) (2026)

## Abstract (arXiv)

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.