A note on the improved sparse Hanson-Wright inequalities
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915523482091520 |
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| author | Dai, Guozheng He, Yiyun Wang, Ke Zhu, Yizhe |
| author_facet | Dai, Guozheng He, Yiyun Wang, Ke Zhu, Yizhe |
| contents | We establish sparse Hanson-Wright inequalities for quadratic forms of sparse $α$-sub-exponential random vectors with exponent parameter $α\in(0, 2]$. In the regime $0< α\le 1$ we derive a refined inequality that is optimal in several canonical models. These results extend the classical Hanson-Wright bound to the sparse setting. Illustrative applications include covariance matrix estimation with incomplete observations, low-rank matrix approximation under the maximum norm with sparsified sketches, and concentration inequalities for sparse $α$-sub-exponential random vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the improved sparse Hanson-Wright inequalities Dai, Guozheng He, Yiyun Wang, Ke Zhu, Yizhe Probability We establish sparse Hanson-Wright inequalities for quadratic forms of sparse $α$-sub-exponential random vectors with exponent parameter $α\in(0, 2]$. In the regime $0< α\le 1$ we derive a refined inequality that is optimal in several canonical models. These results extend the classical Hanson-Wright bound to the sparse setting. Illustrative applications include covariance matrix estimation with incomplete observations, low-rank matrix approximation under the maximum norm with sparsified sketches, and concentration inequalities for sparse $α$-sub-exponential random vectors. |
| title | A note on the improved sparse Hanson-Wright inequalities |
| topic | Probability |
| url | https://arxiv.org/abs/2505.20799 |