Bayesian mixture models (in)consistency for the number of clusters - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement
Article Dans Une Revue Scandinavian Journal of Statistics Année : 2024

Bayesian mixture models (in)consistency for the number of clusters

Résumé

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well‐suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of components is finite, for the Dirichlet process and Pitman–Yor process mixture models. We extend these results to additional Bayesian nonparametric priors such as Gibbs‐type processes and finite‐dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman–Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a postprocessing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.

Dates et versions

hal-04660800 , version 1 (24-07-2024)

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Louise Alamichel, Daria Bystrova, Julyan Arbel, Guillaume Kon Kam King. Bayesian mixture models (in)consistency for the number of clusters. Scandinavian Journal of Statistics, 2024, 51 (4), pp.1619-1660. ⟨10.1111/sjos.12739⟩. ⟨hal-04660800⟩
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