Robust Gradient Descent Estimation for Tensor Models under Heavy-Tailed Distributions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912586699636736 |
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| author | Zhang, Xiaoyu Wang, Di Li, Guodong Sun, Defeng |
| author_facet | Zhang, Xiaoyu Wang, Di Li, Guodong Sun, Defeng |
| contents | Low-rank tensor models are widely used in statistics. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04773 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Gradient Descent Estimation for Tensor Models under Heavy-Tailed Distributions Zhang, Xiaoyu Wang, Di Li, Guodong Sun, Defeng Methodology Low-rank tensor models are widely used in statistics. 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. |
| title | Robust Gradient Descent Estimation for Tensor Models under Heavy-Tailed Distributions |
| topic | Methodology |
| url | https://arxiv.org/abs/2412.04773 |