# Estimating leverage scores via rank revealing methods and randomization

@article{Sobczyk2021EstimatingLS, title={Estimating leverage scores via rank revealing methods and randomization}, author={Aleksandros Sobczyk and Efstratios Gallopoulos}, journal={ArXiv}, year={2021}, volume={abs/2105.11004} }

We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction transforms. We first develop a set of fast novel algorithms for rank estimation, column subset selection and least squares preconditioning. We then describe the design and implementation of leverage score estimators based on these primitives…

## 3 Citations

### A quantum-inspired algorithm for approximating statistical leverage scores

- Computer ScienceArXiv
- 2021

This work proposes a quantum-inspired algorithm for approximating the statistical leverage scores of a matrix A and shows that this algorithm takes time polynomial in an integer k, condition number κ and logarithm of the matrix size.

### pylspack: Parallel algorithms and data structures for sketching, column subset selection, regression and leverage scores

- Computer ScienceACM Transactions on Mathematical Software
- 2022

This work presents parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra, with a special focus on “tall-and-skinny” matrices, which arise in many applications.

### Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss

- Computer ScienceArXiv
- 2022

An algorithm to estimate the Euclidean lengths of the rows of a matrix and proves element-wise probabilistic bounds that are at least as good as standard JL approximations in the worst-case, but are asymptotically better for matrices with decaying spectrum.

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