Exact Recovery of Stochastic Block Model by Ising Model

Zhao, Feng; Ye, Min; Huang, Shao-Lun

doi:10.3390/e23010065

Open AccessArticle

Exact Recovery of Stochastic Block Model by Ising Model

by

Feng Zhao

^1,†

,

Min Ye

^2,† and

Shao-Lun Huang

^2,*

¹

Department of Electronics, Tsinghua University, Beijing 100084, China

²

Tsinghua Berkeley Shenzhen Institute, Berkeley, CA 94704, USA

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Entropy 2021, 23(1), 65; https://doi.org/10.3390/e23010065

Submission received: 29 November 2020 / Revised: 20 December 2020 / Accepted: 30 December 2020 / Published: 2 January 2021

(This article belongs to the Special Issue Phase Transitions and Emergent Phenomena: How Change Emerges through Basic Probability Models)

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Abstract

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.

Keywords: stochastic block model; exact recovery; Ising model; maximum likelihood; metropolis sampling

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MDPI and ACS Style

Zhao, F.; Ye, M.; Huang, S.-L. Exact Recovery of Stochastic Block Model by Ising Model. Entropy 2021, 23, 65. https://doi.org/10.3390/e23010065

AMA Style

Zhao F, Ye M, Huang S-L. Exact Recovery of Stochastic Block Model by Ising Model. Entropy. 2021; 23(1):65. https://doi.org/10.3390/e23010065

Chicago/Turabian Style

Zhao, Feng, Min Ye, and Shao-Lun Huang. 2021. "Exact Recovery of Stochastic Block Model by Ising Model" Entropy 23, no. 1: 65. https://doi.org/10.3390/e23010065

APA Style

Zhao, F., Ye, M., & Huang, S.-L. (2021). Exact Recovery of Stochastic Block Model by Ising Model. Entropy, 23(1), 65. https://doi.org/10.3390/e23010065

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Exact Recovery of Stochastic Block Model by Ising Model

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