Distributional Determinantal Point Process for Repulsive Clustering of Distributions

• URL: http://arxiv.org/abs/2607.21847v1
• Date: Thu, 23 Jul 2026 22:32:00 GMT
• Title: Distributional Determinantal Point Process for Repulsive Clustering of Distributions
• Abstract summary: We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process.<n>We show its validity as a well-defined point process.<n>We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters.
• Score: 23.41791057002045
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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