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Analysis of networks via the sparse β-Model
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Chen, Mingli, Kato, Kengo and Leng, Chenlei (2021) Analysis of networks via the sparse β-Model. Journal of the Royal Statistical Society : Series B (Statistical Methodology), 83 (5). pp. 887-910. doi:10.1111/rssb.12444 ISSN 1369-7412.
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Official URL: https://doi.org/10.1111/rssb.12444
Abstract
Data in the form of networks are increasingly available in a variety of areas, yet statistical models allowing for parameter estimates with desirable statistical properties for sparse networks remain scarce. To address this, we propose the Sparse β-Model (SβM), a new network model that interpolates the celebrated Erdős-Rényi model and the β-model that assigns one different parameter to each node. By a novel reparameterization of the β-model to distinguish global and local parameters, our SβM can drastically reduce the dimensionality of the β-model by requiring some of the local parameters to be zero. We derive the asymptotic distribution of the maximum likelihood estimator of the SβM when the support of the parameter vector is known. When the support is unknown, we formulate a penalized likelihood approach with the ℓ0-penalty. Remarkably, we show via a monotonicity lemma that the seemingly combinatorial computational problem due to the ℓ0-penalty can be overcome by assigning nonzero parameters to those nodes with the largest degrees. We further show that a β-min condition guarantees our method to identify the true model and provide excess risk bounds for the estimated parameters. The estimation procedure enjoys good finite sample properties as shown by simulation studies. The usefulness of the SβM is further illustrated via the analysis of a microfinance take up example.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Social Sciences > Economics Faculty of Science, Engineering and Medicine > Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Computer networks, Random graphs | ||||||||||||
| Journal or Publication Title: | Journal of the Royal Statistical Society : Series B (Statistical Methodology) | ||||||||||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||||||
| ISSN: | 1369-7412 | ||||||||||||
| Official Date: | 23 November 2021 | ||||||||||||
| Dates: |
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| Volume: | 83 | ||||||||||||
| Number: | 5 | ||||||||||||
| Page Range: | pp. 887-910 | ||||||||||||
| DOI: | 10.1111/rssb.12444 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Copyright Holders: | © 2021 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society | ||||||||||||
| Date of first compliant deposit: | 28 August 2019 | ||||||||||||
| Date of first compliant Open Access: | 28 August 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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