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Robust and Optimal Tensor Estimation via Robust Gradient Descent
| العنوان: | Robust and Optimal Tensor Estimation via Robust Gradient Descent |
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| المؤلفون: | Zhang, Xiaoyu, Wang, Di, Li, Guodong, Sun, Defeng |
| سنة النشر: | 2024 |
| المجموعة: | Statistics |
| مصطلحات موضوعية: | Statistics - Methodology |
| الوصف: | 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, we propose a novel robust estimation procedure based on truncated gradient descent for general low-rank tensor models. We establish the computational convergence of the proposed method and derive optimal statistical rates 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, we present numerical results to demonstrate the effectiveness of our method. Comment: 47 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2412.04773 |
| رقم الانضمام: | edsarx.2412.04773 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |