Covariate-Dependent Clustering of Undirected Networks with Brain-Imaging Data

This article focuses on model-based clustering of subjects based on the shared relationships of subject-specific networks and covariates in scenarios when there are differences in the relationship between networks and covariates for different groups of subjects. It is also of interest to identify the network nodes significantly associated with each covariate in each cluster of subjects. To address these methodological questions, we propose a novel nonparametric Bayesian mixture modeling framework with an undirected network response and scalar predictors. The symmetric matrix coefficients corresponding to the scalar predictors of interest in each mixture component involve low-rankness and group sparsity within the low-rank structure. While the low-rank structure in the network coefficients adds parsimony and computational efficiency, the group sparsity within the low-rank structure enables drawing inference on network nodes and cells significantly associated with each scalar predictor. Being a principled Bayesian mixture modeling framework, our approach allows model-based identification of the number of clusters, offers clustering uncertainty in terms of the co-clustering matrix and presents precise characterization of uncertainty in identifying network nodes significantly related to a predictor in each cluster. Empirical results in various simulation scenarios illustrate substantial inferential gains of the proposed framework in comparison with competitors. Analysis of a real brain connectome dataset using the proposed method provides interesting insights into the brain regions of interest (ROIs) significantly related to creative achievement in each cluster of subjects. Supplementary material shows the convergence rate for the posterior predictive density of the proposed model, additional simulation examples with model misspecification, full conditional distributions to run the Markov chain Monte Carlo (MCMC) algorithm and also presents traceplots for various model parameters to demonstrate convergence of the MCMC algorithm.

本文聚焦于存在群体差异场景下，基于受试者专属网络与协变量（covariates）的共享关联开展基于模型的受试者聚类任务。针对不同受试者群体，其网络与协变量间的关联模式存在显著差异，本研究同时旨在识别各受试者聚类中与每个协变量显著相关的网络节点。为解决上述方法论问题，我们提出一种全新的非参数贝叶斯混合建模框架，该框架以无向网络响应（undirected network response）与标量预测变量（scalar predictors）为建模对象。每个混合分量中对应目标标量预测变量的对称矩阵系数，同时具备低秩性与低秩结构内的组稀疏性（group sparsity）。网络系数中的低秩结构可提升模型的简约性与计算效率，而低秩结构内的组稀疏性则支持针对与各标量预测变量显著相关的网络节点及矩阵单元开展统计推断。作为一套严谨的贝叶斯混合建模框架，本方法可基于模型自动识别聚类数目，可通过共聚类矩阵（co-clustering matrix）量化聚类不确定性，并能精准刻画在每个聚类中识别与预测变量显著相关的网络节点时的推断不确定性。多种仿真场景下的实证结果表明，相较于现有同类竞争方法，所提框架的推断性能获得了显著提升。使用所提方法对真实脑连接组数据集（brain connectome dataset）进行分析，可得到不同受试者聚类中与创造性成就显著相关的感兴趣脑区（regions of interest, ROIs）的富有价值的研究洞察。补充材料展示了所提模型的后验预测密度收敛速率、模型误设定场景下的额外仿真示例、用于运行马尔可夫链蒙特卡洛（Markov chain Monte Carlo, MCMC）算法的全条件分布，以及各类模型参数的轨迹图以验证MCMC算法的收敛性。