Kavli Affiliate: Ke Wang
| First 5 Authors: Guozheng Dai, Guozheng Dai, , ,
| Summary:
We establish sparse Hanson-Wright inequalities for quadratic forms of sparse
$alpha$-sub-exponential random vectors with exponent parameter $alphain(0,
2]$. In the regime $0< alphale 1$ 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 $alpha$-sub-exponential random vectors.
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