Joint modeling of multiview graphs with a common set of nodes between views and auxiliary predictors is an essential, yet less explored, area in statistical methodology. Traditional approaches often treat graphs in different views as independent or fail to adequately incorporate predictors, potentially missing complex dependencies within and across graph views and leading to reduced inferential accuracy. Motivated by such methodological shortcomings, we introduce an integrative Bayesian approach for joint learning of a multiview graph with vector-valued predictors. Our modeling framework assumes a common set of nodes for each graph view while allowing for diverse interconnections or edge weights between nodes across graph views, accommodating both binary and continuous valued edge weights. By adopting a hierarchical Bayesian modeling approach, our framework seamlessly integrates information from diverse graphs through carefully designed prior distributions on model parameters. This approach enables the estimation of crucial model parameters defining the relationship between these graph views and predictors, as well as offers predictive inference of the graph views. Crucially, the approach provides uncertainty quantification in all such inferences. Theoretical analysis establishes that the posterior predictive density for our model asymptotically converges to the true data-generating density, under mild assumptions on the true data-generating density and the growth of the number of graph nodes relative to the sample size. Simulation studies validate the inferential advantages of our approach over predictor-dependent tensor learning and independent learning of different graph views with predictors. We further illustrate model utility by analyzing functional connectivity graphs in neuroscience under cognitive control tasks, relating task-related brain connectivity with phenotypic measures.

翻译：与协变量联合建模的多视图图结构是统计方法学中重要但尚待深化的领域。传统方法常将不同视图的图视为独立实体，或未能充分整合协变量信息，这可能导致忽略图内及跨视图的复杂依赖关系，降低推断准确性。针对这些方法论缺陷，我们提出一种融合向量型协变量的多视图图联合学习贝叶斯框架。该模型假设每个图视图共享相同的节点集，但允许不同视图间节点具有差异化的连接结构或边权重，同时支持二值型和连续型边权重。通过采用分层贝叶斯建模策略，我们借助精心设计的参数先验分布，有机整合来自不同视图的图结构信息。该框架既能估计定义图视图与协变量关系的关键参数，又可实现图视图的预测推断，尤为重要的是能为所有推断结果提供不确定性量化。理论分析表明，在真实数据生成密度和相对于样本量的图节点数量增长的温和假设下，模型的后验预测密度渐近收敛于真实数据生成密度。模拟研究证实，相较于协变量依赖的张量学习及不同图视图的独立学习方法，本方法具有显著推断优势。我们进一步通过分析认知控制任务下的脑功能连接网络，揭示了任务相关脑连接与表型测量指标的关联，验证了模型的实际应用价值。