Open Access
2020 Exact recovery in block spin Ising models at the critical line
Matthias Löwe, Kristina Schubert
Electron. J. Statist. 14(1): 1796-1815 (2020). DOI: 10.1214/20-EJS1703


We show how to exactly reconstruct the block structure at the critical line in the so-called Ising block model. This model was recently re-introduced by Berthet, Rigollet and Srivastava in [2]. There the authors show how to exactly reconstruct blocks away from the critical line and they give an upper and a lower bound on the number of observations one needs; thereby they establish a minimax optimal rate (up to constants). Our technique relies on a combination of their methods with fluctuation results obtained in [20]. The latter are extended to the full critical regime. We find that the number of necessary observations depends on whether the interaction parameter between two blocks is positive or negative: In the first case, there are about $N\log N$ observations required to exactly recover the block structure, while in the latter case $\sqrt{N}\log N$ observations suffice.


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Matthias Löwe. Kristina Schubert. "Exact recovery in block spin Ising models at the critical line." Electron. J. Statist. 14 (1) 1796 - 1815, 2020.


Received: 1 June 2019; Published: 2020
First available in Project Euclid: 24 April 2020

zbMATH: 07200244
MathSciNet: MR4090785
Digital Object Identifier: 10.1214/20-EJS1703

Keywords: Block models , Critical temperature , Curie-Weiss model , Fluctuations , Ising model

Vol.14 • No. 1 • 2020
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