论文标题
使用数据扩展的张量值观测值确定张张值的观测值
Order Determination for Tensor-valued Observations Using Data Augmentation
论文作者
论文摘要
张力值数据的降低量的缩小在模式数量中的指数呈指数呈指数，从而极大地受益于尺寸。为了实现最大程度的减少而不会损失信息，我们的目的是为最佳选择降低维度提供自动化程序。我们的方法将最近提出的数据增强程序与高阶奇异值分解（HOSVD）结合在一起。我们给出了有关如何选择调整参数并在模拟研究中进一步检查其影响力的理论准则。作为我们的主要结果，我们表明该过程始终估算在嘈杂的张量模型下的真正潜在维度，无论是种群和样本水平。此外，我们提出了一种基于自动启动的替代增强估计器的替代方案。模拟用于证明在各种设置下两种方法的估计精度。
Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated procedure for the optimal selection of the reduced dimensionality. Our approach combines a recently proposed data augmentation procedure with the higher-order singular value decomposition (HOSVD) in a tensorially natural way. We give theoretical guidelines on how to choose the tuning parameters and further inspect their influence in a simulation study. As our primary result, we show that the procedure consistently estimates the true latent dimensions under a noisy tensor model, both at the population and sample levels. Additionally, we propose a bootstrap-based alternative to the augmentation estimator. Simulations are used to demonstrate the estimation accuracy of the two methods under various settings.
