Uncertainty quantification for mixed membership in multilayer networks with degree heterogeneity using Gaussian variational inference
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| Format: | Preprint |
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2025
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| _version_ | 1866912755034882048 |
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| author | Xie, Fangzheng Huang, Hsin-Hsiung |
| author_facet | Xie, Fangzheng Huang, Hsin-Hsiung |
| contents | Analyzing multilayer networks is central to understanding complex relational measurements collected across multiple conditions or over time. A pivotal task in this setting is to quantify uncertainty in community structure while appropriately pooling information across layers and accommodating layer-specific heterogeneity. Building on the multilayer degree-corrected mixed-membership (ML-DCMM) model, which captures both stable community membership profiles and layer-specific vertex activity levels, we propose a Bayesian inference framework based on a spectral-assisted likelihood. We then develop a computationally efficient Gaussian variational inference algorithm implemented via stochastic gradient descent. Our theoretical analysis establishes a variational Bernstein--von Mises theorem, which provides a frequentist guarantee for using the variational posterior to construct confidence sets for mixed memberships. We demonstrate the utility of the method on a U.S. airport longitudinal network, where the procedure yields robust estimates, natural uncertainty quantification, and competitive performance relative to state-of-the-art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty quantification for mixed membership in multilayer networks with degree heterogeneity using Gaussian variational inference Xie, Fangzheng Huang, Hsin-Hsiung Methodology Statistics Theory Computation Analyzing multilayer networks is central to understanding complex relational measurements collected across multiple conditions or over time. A pivotal task in this setting is to quantify uncertainty in community structure while appropriately pooling information across layers and accommodating layer-specific heterogeneity. Building on the multilayer degree-corrected mixed-membership (ML-DCMM) model, which captures both stable community membership profiles and layer-specific vertex activity levels, we propose a Bayesian inference framework based on a spectral-assisted likelihood. We then develop a computationally efficient Gaussian variational inference algorithm implemented via stochastic gradient descent. Our theoretical analysis establishes a variational Bernstein--von Mises theorem, which provides a frequentist guarantee for using the variational posterior to construct confidence sets for mixed memberships. We demonstrate the utility of the method on a U.S. airport longitudinal network, where the procedure yields robust estimates, natural uncertainty quantification, and competitive performance relative to state-of-the-art methods. |
| title | Uncertainty quantification for mixed membership in multilayer networks with degree heterogeneity using Gaussian variational inference |
| topic | Methodology Statistics Theory Computation |
| url | https://arxiv.org/abs/2512.08146 |