In this article, we propose a Bayesian nonparametric model for clustering grouped data. We adopt a hierarchical approach: at the highest level, each group of data is modeled according to a mixture, where the mixing distributions are conditionally independent normalized completely random measures (NormCRMs) centered on the same base measure, which is itself a NormCRM. The discreteness of the shared base measure implies that the processes at the data level share the same atoms. This desired feature allows to cluster together observations of different groups. We obtain a representation of the hierarchical clustering model by marginalizing with respect to the infinite dimensional NormCRMs. We investigate the properties of the clustering structure induced by the proposed model and provide theoretical results concerning the distribution of the number of clusters, within and between groups. Furthermore, we offer an interpretation in terms of generalized Chinese restaurant franchise process, which allows for posterior inference under both conjugate and nonconjugate models. We develop algorithms for fully Bayesian inference and assess performances by means of a simulation study and a real-data illustration. Supplementary materials for this article are available online.

Argiento, R., Cremaschi, A., Vannucci, M., Hierarchical Normalized Completely Random Measures to Cluster Grouped Data, <<JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION>>, 2019; (NA): 1-26. [doi:10.1080/01621459.2019.1594833] [http://hdl.handle.net/10807/146653]

Hierarchical Normalized Completely Random Measures to Cluster Grouped Data

Argiento, Raffaele
Primo
;
2019

Abstract

In this article, we propose a Bayesian nonparametric model for clustering grouped data. We adopt a hierarchical approach: at the highest level, each group of data is modeled according to a mixture, where the mixing distributions are conditionally independent normalized completely random measures (NormCRMs) centered on the same base measure, which is itself a NormCRM. The discreteness of the shared base measure implies that the processes at the data level share the same atoms. This desired feature allows to cluster together observations of different groups. We obtain a representation of the hierarchical clustering model by marginalizing with respect to the infinite dimensional NormCRMs. We investigate the properties of the clustering structure induced by the proposed model and provide theoretical results concerning the distribution of the number of clusters, within and between groups. Furthermore, we offer an interpretation in terms of generalized Chinese restaurant franchise process, which allows for posterior inference under both conjugate and nonconjugate models. We develop algorithms for fully Bayesian inference and assess performances by means of a simulation study and a real-data illustration. Supplementary materials for this article are available online.
2019
Inglese
Argiento, R., Cremaschi, A., Vannucci, M., Hierarchical Normalized Completely Random Measures to Cluster Grouped Data, <<JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION>>, 2019; (NA): 1-26. [doi:10.1080/01621459.2019.1594833] [http://hdl.handle.net/10807/146653]
File in questo prodotto:
File Dimensione Formato  
Hierarchical-Normalized-Completely-Random-Measures-to-Cluster-Grouped-Data2020Journal-of-the-American-Statistical-Association.pdf

non disponibili

Tipologia file ?: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 2.78 MB
Formato Unknown
2.78 MB Unknown   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/146653
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 12
social impact