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Estimating network edge probabilities by neighbourhood smoothing

Author

Listed:
  • Yuan Zhang
  • Elizaveta Levina
  • Ji Zhu

Abstract

SummaryThe estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.

Suggested Citation

  • Yuan Zhang & Elizaveta Levina & Ji Zhu, 2017. "Estimating network edge probabilities by neighbourhood smoothing," Biometrika, Biometrika Trust, vol. 104(4), pages 771-783.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:4:p:771-783.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx042
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    Citations

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    Cited by:

    1. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Dec 2023.
    2. Yuan, Quan & Liu, Binghui, 2021. "Community detection via an efficient nonconvex optimization approach based on modularity," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    3. Chunning Wang & Fengqin Tang & Xuejing Zhao, 2023. "LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks," Mathematics, MDPI, vol. 11(14), pages 1-15, July.
    4. Eric Auerbach, 2022. "Identification and Estimation of a Partially Linear Regression Model Using Network Data," Econometrica, Econometric Society, vol. 90(1), pages 347-365, January.
    5. Wei Zhao & S.N. Lahiri, 2022. "Estimation of the Parameters in an Expanding Dynamic Network Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 261-282, June.
    6. Yiming Tang & Yang Bai & Tao Huang, 2021. "Network vector autoregression with individual effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 875-893, August.
    7. S Chandna & S C Olhede & P J Wolfe, 2022. "Local linear graphon estimation using covariates [Representations for partially exchangeable arrays of random variables]," Biometrika, Biometrika Trust, vol. 109(3), pages 721-734.
    8. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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