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February 2020 Optimal rates for community estimation in the weighted stochastic block model
Min Xu, Varun Jog, Po-Ling Loh
Ann. Statist. 48(1): 183-204 (February 2020). DOI: 10.1214/18-AOS1797

Abstract

Community identification in a network is an important problem in fields such as social science, neuroscience and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a weighted generalization of the SBM, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints. We characterize the optimal rate of misclustering error of the weighted SBM in terms of the Renyi divergence of order 1/2 between the weight distributions of within-community and between-community edges, substantially generalizing existing results for unweighted SBMs. Furthermore, we present a computationally tractable algorithm based on discretization that achieves the optimal error rate. Our method is adaptive in the sense that the algorithm, without assuming knowledge of the weight densities, performs as well as the best algorithm that knows the weight densities.

Citation

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Min Xu. Varun Jog. Po-Ling Loh. "Optimal rates for community estimation in the weighted stochastic block model." Ann. Statist. 48 (1) 183 - 204, February 2020. https://doi.org/10.1214/18-AOS1797

Information

Received: 1 June 2017; Revised: 1 September 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196535
MathSciNet: MR4065158
Digital Object Identifier: 10.1214/18-AOS1797

Subjects:
Primary: 62H30, 91D30
Secondary: 62C20, 90B15

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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