论文标题
张量PCA的电源迭代
Power Iteration for Tensor PCA
论文作者
论文摘要
在本文中，我们研究了[44]中介绍的尖峰张量模型的功率迭代算法。我们为电源迭代算法的收敛提供了必要的条件。当功率迭代算法收敛时，对于等级的一个尖刺张量模型，我们显示了信号的尖峰强度和线性函数的估计器，是渐近的高斯。对于多级尖刺张量模型，我们显示估计量是高斯的渐近混合物。这种新现象与加标矩阵模型不同。使用这些估计器的这些渐近结果，我们为信号的尖峰强度和线性功能构建有效有效的置信区间。
In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the power iteration algorithm. When the power iteration algorithm converges, for the rank one spiked tensor model, we show the estimators for the spike strength and linear functionals of the signal are asymptotically Gaussian; for the multi-rank spiked tensor model, we show the estimators are asymptotically mixtures of Gaussian. This new phenomenon is different from the spiked matrix model. Using these asymptotic results of our estimators, we construct valid and efficient confidence intervals for spike strengths and linear functionals of the signals.
