{"ID":2830961,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08146","arxiv_id":"2512.08146","title":"Uncertainty quantification for mixed membership in multilayer networks with degree heterogeneity using Gaussian variational inference","abstract":"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.","short_abstract":"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 heterogenei...","url_abs":"https://arxiv.org/abs/2512.08146","url_pdf":"https://arxiv.org/pdf/2512.08146v1","authors":"[\"Fangzheng Xie\",\"Hsin-Hsiung Huang\"]","published":"2025-12-09T00:58:58Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"stat.CO\"]","methods":"[]","has_code":false}