Convergence of the groups posterior distribution in latent or stochastic block models - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2015

Convergence of the groups posterior distribution in latent or stochastic block models

Résumé

We propose a unified framework for studying both latent and stochastic block models, which are used to cluster simultaneously rows and columns of a data matrix. In this new framework, we study the behaviour of the groups posterior distribution, given the data. We characterize whether it is possible to asymptotically recover the actual groups on the rows and columns of the matrix, relying on a consistent estimate of the parameter. In other words, we establish sufficient conditions for the groups posterior distribution to converge (as the size of the data increases) to a Dirac mass located at the actual (random) groups configuration. In particular, we highlight some cases where the model assumes symmetries in the matrix of connection probabilities that prevents recovering the original groups. We also discuss the validity of these results when the proportion of non-null entries in the data matrix converges to zero.
Fichier principal
Vignette du fichier
posterior_blockmodels_revised.pdf (376.14 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00713120 , version 1 (29-06-2012)
hal-00713120 , version 2 (09-08-2013)

Identifiants

Citer

Mahendra Mariadassou, Catherine Matias. Convergence of the groups posterior distribution in latent or stochastic block models. Bernoulli, 2015, 21 (1), pp.537-573. ⟨hal-00713120v2⟩
447 Consultations
199 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More