论文标题
椭圆形的张量变化分布，并应用于改进图像学习
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learning
论文作者
论文摘要
张量值数据的统计分析已在很大程度上使用了张量变化的正常（TVN）分布，而当数据来自具有更重或较轻的尾巴的分布时，可能是不够的。我们研究了椭圆形的（EC）张量变化分布的一般家族，并得出其特征，力矩，边际和条件分布以及EC WishArt分布。我们描述了（1）从EC分布中的数据，（2）从TVN分布的比例混合物以及（3）从基本但未知的EC分布中的比例混合物中描述（1）不相关的绘制程序，以最大程度地估算了最大似然性估计的程序。一项详细的仿真研究突出了选择EC分布而不是TVN的较重数据的好处。我们使用判别分析和EC错误制定张量变化的分类规则，并表明它们比基于TVN的规则更好地预测动物面部图像中的猫和狗。在EC错误下，在EC错误下进行的新型张量调节回归和张量变化分析（Tanova）框架也比通常的野生数据集的著名标签面孔更好地表征了性别，年龄和种族来源。
Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate when data comes from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) tensor-variate distributions and derive its characterizations, moments, marginal and conditional distributions, and the EC Wishart distribution. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, where we extend Tyler's robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop tensor-variate classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and tensor-variate analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age and ethnic origin than the usual TVN-based TANOVA in the celebrated Labeled Faces of the Wild dataset.
