Séance Séminaire

Séminaire de Probabilités et Statistique

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

We propose a unied 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. In other words, we establish sucient 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 conguration. In particular, we highlight some cases where the model assumes symmetries in the matrix of connection probabilities that prevents from a correct recovering of the groups. We also discuss the validity of these results when the proportion of non-null entries in the data matrix converges to zero.