Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2015, Article ID 657965, 14 pages
Research Article

Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm

Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem Rakpart 3, Budapest 1111, Hungary

Received 16 June 2015; Revised 6 November 2015; Accepted 10 November 2015

Academic Editor: Hyungjun Cho

Copyright © 2015 Marianna Bolla and Ahmed Elbanna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a semiparametric block model for graphs, where the within- and between-cluster edge probabilities are not constants within the blocks but are described by logistic type models, reminiscent of the 50-year-old Rasch model and the newly introduced - models. Our purpose is to give a partition of the vertices of an observed graph so that the induced subgraphs and bipartite graphs obey these models, where their strongly interlaced parameters give multiscale evaluation of the vertices at the same time. In this way, a profoundly heterogeneous version of the stochastic block model is built via mixtures of the above submodels, while the parameters are estimated with a special EM iteration.