Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate t-distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet t-distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.

(2019). Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling [journal article - articolo]. In BAYESIAN ANALYSIS. Retrieved from http://hdl.handle.net/10446/193471

Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling

Argiento, Raffaele;
2019-01-01

Abstract

Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate t-distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet t-distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.
articolo
2019
Cremaschi, Andrea; Argiento, Raffaele; Shoemaker, Katherine; Peterson, Christine; Vannucci, Marina
(2019). Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling [journal article - articolo]. In BAYESIAN ANALYSIS. Retrieved from http://hdl.handle.net/10446/193471
File allegato/i alla scheda:
File Dimensione del file Formato  
Bayesian_Analysis_con_Andrea_e_Marina.pdf

accesso aperto

Versione: publisher's version - versione editoriale
Licenza: Creative commons
Dimensione del file 614.55 kB
Formato Adobe PDF
614.55 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Aisberg ©2008 Servizi bibliotecari, Università degli studi di Bergamo | Terms of use/Condizioni di utilizzo

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/193471
Citazioni
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact