论文标题
降低量张量张量回归和张量变化方差分析
Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of Variance
论文作者
论文摘要
与许多多变量响应和协变量的拟合回归模型可能具有挑战性，但是这些响应和协变量有时具有张量变化的结构。我们将经典的多元回归模型扩展到以两种方式利用此类结构：首先，我们将四种类型的低级张量格式施加在回归系数上。其次，我们使用张量变化的正态分布对误差进行建模，该分布在协方差矩阵上施加了可分离的格式。我们通过块 - 删除算法获得最大似然估计器，并得出其计算复杂性和渐近分布。我们的回归框架使我们能够制定方差（Tanova）方法的张量变化分析。当应用于单向Tanova布局中时，该方法使我们能够识别与自杀式示威者或非稳定构想者以及在功能磁共振成像研究中的正，负或死亡声明单词的相互作用显着相关的脑区域。另一个应用程序在野生图像数据集的标记面上使用三向塔诺瓦，以区分与种族起源，年龄段和性别有关的面部特征。
Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such structure in two ways: first, we impose four types of low-rank tensor formats on the regression coefficients. Second, we model the errors using the tensor-variate normal distribution that imposes a Kronecker separable format on the covariance matrix. We obtain maximum likelihood estimators via block-relaxation algorithms and derive their computational complexity and asymptotic distributions. Our regression framework enables us to formulate tensor-variate analysis of variance (TANOVA) methodology. This methodology, when applied in a one-way TANOVA layout, enables us to identify cerebral regions significantly associated with the interaction of suicide attempters or non-attemptor ideators and positive-, negative- or death-connoting words in a functional Magnetic Resonance Imaging study. Another application uses three-way TANOVA on the Labeled Faces in the Wild image dataset to distinguish facial characteristics related to ethnic origin, age group and gender.
