论文标题
关于热门型张量的准确性：随机张量分析
On the Accuracy of Hotelling-Type Tensor Deflation: A Random Tensor Analysis
论文作者
论文摘要
在随机张量理论的最新进展中，我们在本文中考虑了$ \ sum_ {i = 1}^rβ_ia_i a_i + w $的等级$ r $不对称的刺激张量模型，其中$β_i\ geq 0 $ and $ a_i $是$ \ a_i $是$ \ \ \ \ lang的$ \ langy a_i， 1] $ for $ i \ neq j $，基于我们提供了大维度中的酒店型张量张量的渐近研究。具体而言，我们的分析表征了渐近张量的张量尺寸，在通缩过程的每个步骤中的奇异值和对齐。这可以用于构建基本问题中涉及的不同数量的一致估计器，例如信噪比$β_I$或不同信号组件之间的对齐$ \ langle a_i，a_j \ rangle $。
Leveraging on recent advances in random tensor theory, we consider in this paper a rank-$r$ asymmetric spiked tensor model of the form $\sum_{i=1}^r β_i A_i + W$ where $β_i\geq 0$ and the $A_i$'s are rank-one tensors such that $\langle A_i, A_j \rangle\in [0, 1]$ for $i\neq j$, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios $β_i$ or the alignments between the different signal components $\langle A_i, A_j \rangle$.
