Bayesian Generalized Sparse Symmetric Tensor-on-Vector Regression
Bayesian Generalized Sparse Symmetric Tensor-on-Vector Regression
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DOI：
10.1080/00401706.2020.1784799
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发表时间：
2020-07-18
期刊：
影响因子：
2.5
通讯作者：
Guhaniyogi, Rajarshi
中科院分区：
文献类型：
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作者：
Guha, Sharmistha;Guhaniyogi, Rajarshi
基于弥散加权磁共振成像（DWI）获得的脑连接体数据集，提出了一种新的广义贝叶斯线性模型框架，该框架具有对称张量响应和标量预测因子。对应于标量预测的对称张量系数嵌入了两个特征：低秩结构中的低秩性和组稀疏性。除了提供计算效率和简约性之外，这两个特征还能够识别与预测因子显著相关的重要“张量节点”和“张量单元”，并表征不确定性。所提出的框架下，各种模拟设置和一个真实的大脑连接体数据集进行了实证研究。从理论上讲，我们建立了所提出的模型的后验预测密度是“接近”的真实数据生成密度，这两个密度之间的海林格距离测量的接近程度，其缩放速度非常接近有限维的最佳速率，这取决于张量节点的数量如何随着样本大小而增长。理论结果与证明提供在这是可在线.
Motivated by brain connectome datasets acquired using diffusion weighted magnetic resonance imaging (DWI), this article proposes a novel generalized Bayesian linear modeling framework with a symmetric tensor response and scalar predictors. The symmetric tensor coefficients corresponding to the scalar predictors are embedded with two features: low-rankness and group sparsity within the low-rank structure. Besides offering computational efficiency and parsimony, these two features enable identification of important "tensor nodes" and "tensor cells" significantly associated with the predictors, with characterization of uncertainty. The proposed framework is empirically investigated under various simulation settings and with a real brain connectome dataset. Theoretically, we establish that the posterior predictive density from the proposed model is "close" to the true data generating density, the closeness being measured by the Hellinger distance between these two densities, which scales at a rate very close to the finite dimensional optimal rate of, depending on how the number of tensor nodes grow with the sample size. The theoretical results with proofs are provided in thewhich are available online.