aiqbench analysis
This paper introduces the distributional determinantal point process (dDPP), a novel mathematical framework for clustering probability distributions rather than individual data points. By leveraging sliced Wasserstein kernels within an L-ensemble structure, it enables repulsive clustering that effectively handles complex datasets like single-cell gene expression and epilepsy records. The work advances machine learning methodology by providing rigorous concentration results for estimators in this distribution-valued setting, offering a new tool for interpretable pattern recognition in high-dimensional spaces.
Distributional Determinantal Point Process for Repulsive Clustering of Distributions
arXiv:2607.21847v1 Announce Type: cross 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.
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.
Methodology (stat.ME); Machine Learning (cs.LG); Applications (stat.AP); Computation (stat.CO); Machine Learning (stat.ML)
arXiv:2607.21847 [stat.ME]
(or arXiv:2607.21847v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2607.21847 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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