This study presents a Bayesian regression framework to model the relationship between scalar outcomes and brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the connectivity predictors thereby ignoring their matrix structures, our method respects the Riemannian geometry of SPD matrices by modelling them in a tangent space. We perform dimension reduction in the tangent space, relating the resulting low-dimensional representations with the responses. The dimension reduction matrix is learnt in a supervised manner with a sparsity-inducing prior imposed on a Stiefel manifold to prevent overfitting. Our method yields a parsimonious regression model that allows uncertainty quantification of the estimates and identification of key brain regions that predict the outcomes. We demonstrate the performance of our approach in simulation settings and through a case study to predict Picture Vocabulary scores using data from the Human Connectome Project.

翻译：本研究提出一种贝叶斯回归框架，用于建模标量结果与以对称正定（SPD）矩阵形式表征的脑功能连接之间的关系。与许多简单地将连接性预测因子向量化而忽略其矩阵结构的方案不同，我们的方法通过在切空间中对SPD矩阵进行建模，尊重其黎曼几何结构。我们在切空间中执行降维，将得到的低维表示与响应变量相关联。该降维矩阵以监督方式学习，并在Stiefel流形上施加稀疏诱导先验以防止过拟合。我们的方法得到简洁的回归模型，能够对估计值进行不确定性量化，并识别预测结果的关键脑区。我们通过模拟实验及一项使用人类连接组项目数据预测图片词汇得分的案例研究，展示了该方法的性能。