Replicated weighted networks often exhibit many structural zeros alongside heterogeneous non-zero edge strengths. In structural connectomics, this zero-inflation coincides with subjects expressing overlapping, rather than discrete, connectivity patterns. To address these features, we propose a Bayesian adaptive latent mixture model for zero-inflated weighted networks. Our approach represents each subject network as a simplex mixture of shared low-rank latent score matrices, integrated with a hurdle likelihood that separates edge existence from conditional edge strength. A sparsity-coupling parameter enables absent edges to be either independent of, or informative about, the latent connectivity. For computation, we employ transformed Hamiltonian Monte Carlo on unconstrained coordinates, selecting the number of templates via predictive fit, held-out link prediction, and template stability. Theoretically, we establish posterior consistency, local asymptotic normality, a Bernstein--von Mises approximation, and predictive consistency for an identifiable quotient-space estimand under a fixed-template scenario. Simulations demonstrate performance gains over topology-only baselines in settings with mixed memberships or structure-informed sparsity. Applied to Human Connectome Project data, the model recovers stable latent score patterns and heterogeneous subject-level mixtures, with behavioural analyses serving strictly as exploratory annotations rather than confirmatory biomarker claims.

翻译：复现加权网络通常表现出大量结构零值，同时伴有异质的非零边强度。在结构连接组学中，这种零膨胀与受试者呈现重叠（而非离散）的连接模式并存。为应对这些特征，我们提出了一种针对零膨胀加权网络的贝叶斯自适应潜在混合模型。该方法将每个受试者网络表示为共享低秩潜在得分矩阵的单纯形混合，并与区分边存在性与条件边强度的障碍似然函数相结合。一个稀疏耦合参数使得缺失边可以独立于潜在连接性，或为其提供信息。在计算方面，我们在无约束坐标上采用变换后的哈密顿蒙特卡洛方法，通过预测拟合度、保留集边预测及模板稳定性来选定模板数量。理论上，我们在固定模板场景下建立了后验一致性、局部渐近正态性、伯恩斯坦-冯·米塞斯近似以及可识别商空间估计量的预测一致性。模拟实验表明，在混合成员身份或结构引导稀疏性设定下，该模型相较仅基于拓扑结构的基线方法具有性能提升。应用于人类连接组项目数据时，该模型恢复了稳定的潜在得分模式和异质的受试者水平混合，其中行为分析严格作为探索性注释而非验证性生物标记声明。