Open Access
2018 Estimating a network from multiple noisy realizations
Can M. Le, Keith Levin, Elizaveta Levina
Electron. J. Statist. 12(2): 4697-4740 (2018). DOI: 10.1214/18-EJS1521


Complex interactions between entities are often represented as edges in a network. In practice, the network is often constructed from noisy measurements and inevitably contains some errors. In this paper we consider the problem of estimating a network from multiple noisy observations where edges of the original network are recorded with both false positives and false negatives. This problem is motivated by neuroimaging applications where brain networks of a group of patients with a particular brain condition could be viewed as noisy versions of an unobserved true network corresponding to the disease. The key to optimally leveraging these multiple observations is to take advantage of network structure, and here we focus on the case where the true network contains communities. Communities are common in real networks in general and in particular are believed to be presented in brain networks. Under a community structure assumption on the truth, we derive an efficient method to estimate the noise levels and the original network, with theoretical guarantees on the convergence of our estimates. We show on synthetic networks that the performance of our method is close to an oracle method using the true parameter values, and apply our method to fMRI brain data, demonstrating that it constructs stable and plausible estimates of the population network.


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Can M. Le. Keith Levin. Elizaveta Levina. "Estimating a network from multiple noisy realizations." Electron. J. Statist. 12 (2) 4697 - 4740, 2018.


Received: 1 October 2017; Published: 2018
First available in Project Euclid: 22 December 2018

zbMATH: 07003255
MathSciNet: MR3894068
Digital Object Identifier: 10.1214/18-EJS1521

Primary: 62H12
Secondary: 62F12 , 62H30

Keywords: brain networks , EM algorithm , Noisy networks , Stochastic block model

Vol.12 • No. 2 • 2018
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