论文标题
张量最小二乘的子采样：优化和统计观点
Subsampling for tensor least squares: Optimization and statistical perspectives
论文作者
论文摘要
在本文中，我们研究了有关流行的T产品的张量最小二乘问题的随机亚采样方法。从优化的角度来看，我们以提议方法获得的残留和解决方案的概率呈现误差界限。从统计的角度来看，我们得出了解决方案的条件和无条件期望和方差的表达，而无条件的期望和方差结合了模型噪声。此外，基于无条件差异，还发现了最佳的子采样概率分布。最后，通过数值实验验证了所提出方法的可行性和有效性以及理论结果的正确性。
In this paper, we investigate the random subsampling method for tensor least squares problem with respect to the popular t-product. From the optimization perspective, we present the error bounds in the sense of probability for the residual and solution obtained by the proposed method. From the statistical perspective, we derive the expressions of the conditional and unconditional expectations and variances for the solution, where the unconditional ones combine the model noises. Moreover, based on the unconditional variance, an optimal subsampling probability distribution is also found. Finally, the feasibility and effectiveness of the proposed method and the correctness of the theoretical results are verified by numerical experiments.
