论文标题
通过剪接和Huber损失进行稳健的低级张量回归
Robust low-rank tensor regression via clipping and Huber loss
论文作者
论文摘要
在本文中，我们基于截断方法和Huber损失在稳健的低级张量回归下构建了一个参数估计框架，并在随机噪声下研究了稳健的低级张量回归模型，仅有有限的二阶时刻。通过梯度下降方法，我们提出的Huber型强构估计器在两个方面在理论上是最佳的：（1）我们的统计误差率几乎与在高斯误差下传统最小二乘法所述的最佳上限相同； （2）恢复张量参数的样品复杂性也是最佳的。广泛的数值实验表明了我们的估计量的鲁棒性，截断和Huber损失的利用对提高提出的算法的稳定性和统计有效性有益，这比最小二乘方法优于最小二乘方法。同时，通过模拟证实了相位稳健估计器收敛速率中相变的现象。此外，我们将此估计技术应用于图像压缩，这表明我们的方法更有效。
In this paper, we construct a parameter estimation framework under robust low-rank tensor regression based on the truncation method and Huber loss, and study robust low-rank tensor regression model under random noise with only finite second-order moment. Through the gradient descent method, our proposed Huber-type robust estimator is theoretically optimal in two aspects: (1) our statistical error rate is nearly the same as the optimal upper bound deduced by the traditional least squares method under sub-Gaussian error; (2) the sample complexity of recovering the tensor parameter is also optimal. Extensive numerical experiments show the robustness of our estimator, and the utilization of truncation and Huber loss is beneficial to improve the stability and statistical effectiveness of the proposed algorithm which is superior to the least squares method. Meanwhile, the phenomenon of phase transition in the convergence rate of the proposed robust estimator is confirmed through simulation. Furthermore, we apply this estimation technique to image compression, which demonstrates that our method is more effective.
