Exact recovery in block spin Ising models at the critical line

被引:3
|
作者
Loewe, Matthias [1 ]
Schubert, Kristina [2 ]
机构
[1] Univ Munster, Fachbereich Math & Informat, Orleans Ring 10, D-48149 Munster, Germany
[2] Tech Univ Dortmund, Fak Math, Vogelpothsweg 87, D-44227 Dortmund, Germany
来源
ELECTRONIC JOURNAL OF STATISTICS | 2020年 / 14卷 / 01期
关键词
Block models; Ising model; Curie-Weiss model; fluctuations; critical temperature; CURIE-WEISS MODEL; RECONSTRUCTION;
D O I
10.1214/20-EJS1703
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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 root N log N observations suffice.
引用
收藏
页码:1796 / 1815
页数:20
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