Scale-Invariant Robust Estimation of High-Dimensional Kronecker-Structured Matrices
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908727835099136 |
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| author | Zhang, Xiaoyu Fan, Zhiyun Zhang, Wenyang Wang, Di |
| author_facet | Zhang, Xiaoyu Fan, Zhiyun Zhang, Wenyang Wang, Di |
| contents | High-dimensional Kronecker-structured estimation faces a conflict between non-convex scaling ambiguities and statistical robustness. The arbitrary factor scaling distorts gradient magnitudes, rendering standard fixed-threshold robust methods ineffective. We resolve this via Scaled Robust Gradient Descent (SRGD), which stabilizes optimization by de-scaling gradients before truncation. To further enforce interpretability, we introduce Scaled Hard Thresholding (SHT) for invariant variable selection. A two-step estimation procedure, built upon robust initialization and SRGD--SHT iterative updates, is proposed for canonical matrix problems, such as trace regression, matrix GLMs, and bilinear models. The convergence rates are established for heavy-tailed predictors and noise, identifying a phase transition where optimal convergence rates recover under finite noise variance and degrade optimally for heavier tails. Experiments on simulated data and two real-world applications confirm superior robustness and efficiency of the proposed procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scale-Invariant Robust Estimation of High-Dimensional Kronecker-Structured Matrices Zhang, Xiaoyu Fan, Zhiyun Zhang, Wenyang Wang, Di Methodology High-dimensional Kronecker-structured estimation faces a conflict between non-convex scaling ambiguities and statistical robustness. The arbitrary factor scaling distorts gradient magnitudes, rendering standard fixed-threshold robust methods ineffective. We resolve this via Scaled Robust Gradient Descent (SRGD), which stabilizes optimization by de-scaling gradients before truncation. To further enforce interpretability, we introduce Scaled Hard Thresholding (SHT) for invariant variable selection. A two-step estimation procedure, built upon robust initialization and SRGD--SHT iterative updates, is proposed for canonical matrix problems, such as trace regression, matrix GLMs, and bilinear models. The convergence rates are established for heavy-tailed predictors and noise, identifying a phase transition where optimal convergence rates recover under finite noise variance and degrade optimally for heavier tails. Experiments on simulated data and two real-world applications confirm superior robustness and efficiency of the proposed procedure. |
| title | Scale-Invariant Robust Estimation of High-Dimensional Kronecker-Structured Matrices |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.19273 |