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Conference Papers Year : 2023

Clustering inconsistency for Pitman--Yor mixture models with a prior on the precision but fixed discount parameter

Abstract

Bayesian nonparametric (BNP) mixture models such as Dirichlet process (DP) and Pitman-Yor process (PY) mixture models are popular for modeling complex data. Their posterior distributions exhibit nice theoretical properties, converging at the optimal minimax rate to the true data-generating distribution, and extensive research has been devoted to developing this theory. However, consistency of the posterior distribution does not imply consistency of the number of clusters, and asymptotic guarantees for the posterior number of clusters of these BNP mixture models have been lacking until recently. Recent research has shown that these models can be inconsistent for the number of clusters. In the case of DP mixture models, this problem can be avoided when a prior is put on the model's concentration hyperparameter α, as is common practice. In this work, we prove that PY mixture models remain inconsistent for the number of clusters when a prior is put on α, in the special case where the true number of components in the data generating mechanism is equal to 1 and the discount parameter σ ∈ (0, 1) is a fixed constant.
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Dates and versions

hal-04425711 , version 1 (30-01-2024)

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  • HAL Id : hal-04425711 , version 1

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Caroline Lawless, Louise Alamichel, Julyan Arbel, Guillaume Kon Kam King. Clustering inconsistency for Pitman--Yor mixture models with a prior on the precision but fixed discount parameter. AABI 2023 - 5th Symposium on Advances in Approximate Bayesian Inference, Jul 2023, Honolulu, United States. pp.1-12. ⟨hal-04425711⟩
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