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：多视图图（具有视图间公共节点集）与辅助预测变量的联合建模是统计方法论中一个基础但尚未充分探索的领域。传统方法通常将不同视图的图视为独立结构，或未能有效整合预测变量，这可能导致遗漏图内及图间的复杂依赖关系，进而降低推断精度。针对上述方法论缺陷，我们提出了一种整合贝叶斯方法，用于对带有向量值预测变量的多视图图进行联合学习。本建模框架假设每个图视图均具有公共节点集，同时允许不同视图的节点间存在多样化连接或边权重，能够容纳二值型与连续型边权重。通过采纳分层贝叶斯建模策略，该框架借助精心设计的模型参数先验分布，无缝整合来自不同图的信息。该方法不仅能够估计定义图视图与预测变量关系的关键模型参数，还能实现图视图的预测推断。尤为重要的是，该方法可为所有此类推断提供不确定性量化。理论分析表明，在对真实数据生成密度及图节点数量相对样本量增长速率施加温和假设的条件下，本模型的后验预测密度渐近收敛于真实数据生成密度。模拟研究验证了本方法相较于依赖预测变量的张量学习及不同图视图的独立学习（含预测变量）所具有的推断优势。我们进一步通过分析认知控制任务中神经科学的功能连接图，将任务相关脑连接性与表型指标相关联，说明了模型的实际应用价值。