# Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables

arXiv: https://arxiv.org/abs/2209.05685 · HTML: https://mlsanity.com/paper/2209.05685/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2022.

## Built on by (most cited first, 2 of 2)

- [Precise Asymptotic Generalization for Multiclass Classification with Overparameterized Linear Models](https://mlsanity.com/paper/2306.13255/) (2023)
- [ℓ1-Regularized Generalized Least Squares](https://mlsanity.com/paper/2405.10719/) (2024)

## Abstract (arXiv)

In this paper, we derive a new version of Hanson-Wright inequality for a sparse bilinear form of sub-Gaussian variables. Our results are generalization of previous deviation inequalities that consider either sparse quadratic forms or dense bilinear forms. We apply the new concentration inequality to testing the cross-covariance matrix when data are subject to missing. Using our results, we can find a threshold value of correlations that controls the family-wise error rate. Furthermore, we discuss the multiplicative measurement error case for the bilinear form with a boundedness condition.