This paper presents a Bayesian regression model relating scalar outcomes to brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the matrix-valued connectivity predictors thereby ignoring their geometric structure, the method presented here respects the Riemannian geometry of SPD matrices by using a tangent space modeling. Dimension reduction is performed in the tangent space, relating the resulting low-dimensional representations to the responses. The dimension reduction matrix is learned 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 all model parameters 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：本文提出了一种贝叶斯回归模型，用于将标量结果与以对称正定（SPD）矩阵形式表示的脑功能连接相关联。与许多简单地向量化矩阵值连接预测因子而忽略其几何结构的方案不同，本文提出的方法通过使用切空间建模来遵循SPD矩阵的黎曼几何。降维在切空间中进行，将所得的低维表示与响应变量相关联。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。我们的方法产生了一个简约的回归模型，能够对所有模型参数进行不确定性量化，并识别出预测结果的关键脑区。我们通过模拟设置和一项案例研究展示了该方法的性能，该案例研究利用人类连接组项目的数据来预测图片词汇测试分数。