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A note on the improved sparse Hanson-Wright inequalities

Year: 2025

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.20799

Authors: Dai, Guozheng, He, Yiyun, Wang, Ke, Zhu, Yizhe

Institutions: Hong Kong University of Science and Technology, University of Hong Kong, University of California, Irvine, University of Southern California

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415036274

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