A0769
Title: Robust and optimal tensor estimation via robust gradient descent
Authors: Xiaoyu Zhang - Tongji University (China) [presenting]
Abstract: Low-rank tensor models are widely used in statistics and machine learning. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions encountered in real-world applications, a novel, robust estimation procedure is proposed based on truncated gradient descent for general low-rank tensor models. The computational convergence of the proposed method is established, and optimal statistical rates are derived under heavy-tailed distributional settings of both covariates and noise for various low-rank models. Notably, the statistical error rates are governed by a local moment condition, which captures the distributional properties of tensor variables projected onto certain low-dimensional local regions. Furthermore, numerical results are presented to demonstrate the effectiveness of the method.
