论文标题
使用塔克分解进行稀疏空间建模的贝叶斯张量回归
Bayesian tensor regression using the Tucker decomposition for sparse spatial modeling
论文作者
论文摘要
使用多维阵列或张量进行建模通常由于高维度而出现问题。此外，这些结构通常表现出固有的稀疏性，需要使用正则化方法正确地表征张量协变量和标量响应之间的关联。我们提出了一种贝叶斯方法，以使用Tucker Tensor分解有效地对标量响应进行标量响应进行建模，以将空间关系保留在张量系数中，同时减少模型中变化的参数数量并应用正规化方法。分析模拟数据以将模型与最近提出的方法进行比较。包括使用阿尔茨海默氏症数据神经影像计划的数据进行神经影像分析，以说明模型结构在推断中的好处。
Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize an association between a tensor covariate and a scalar response. We propose a Bayesian method to efficiently model a scalar response with a tensor covariate using the Tucker tensor decomposition in order to retain the spatial relationship within a tensor coefficient, while reducing the number of parameters varying within the model and applying regularization methods. Simulated data are analyzed to compare the model to recently proposed methods. A neuroimaging analysis using data from the Alzheimer's Data Neuroimaging Initiative is included to illustrate the benefits of the model structure in making inference.
