Open Access
August 2019 Exact recovery in the Ising blockmodel
Quentin Berthet, Philippe Rigollet, Piyush Srivastava
Ann. Statist. 47(4): 1805-1834 (August 2019). DOI: 10.1214/17-AOS1620


We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising blockmodel, is a perturbation of the mean field approximation of the Ising model known as the Curie–Weiss model: the sites are partitioned into two blocks of equal size and the interaction between those of the same block is stronger than across blocks, to account for more order within each block. We study probabilistic, statistical and computational aspects of this model in the high-dimensional case when the number of sites may be much larger than the sample size.


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Quentin Berthet. Philippe Rigollet. Piyush Srivastava. "Exact recovery in the Ising blockmodel." Ann. Statist. 47 (4) 1805 - 1834, August 2019.


Received: 1 January 2017; Revised: 1 July 2017; Published: August 2019
First available in Project Euclid: 21 May 2019

zbMATH: 07082271
MathSciNet: MR3953436
Digital Object Identifier: 10.1214/17-AOS1620

Primary: 62H30
Secondary: 82B20

Keywords: Curie–Weiss , Ising blockmodel , planted partition , spectral partitioning , stochastic blockmodel

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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