# Fast Generalized Matrix Regression with Applications in Machine Learning

arXiv: https://arxiv.org/abs/1912.12008 · HTML: https://mlsanity.com/paper/1912.12008/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Debiasing Random Oblique Projections for Subsampled OLS and Fast CUR in High Dimensions](https://mlsanity.com/paper/2605.24955/) (2026)

## Abstract (arXiv)

Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast generalized matrix regression algorithm (Fast GMR) which utilizes sketching technique to solve the GMR problem efficiently. Given error parameter 0<ε<1, the Fast GMR algorithm can achieve a (1+ε) relative error with the sketching sizes being of order cO(ε-1/2) for a large group of GMR problems. We apply the Fast GMR algorithm to the symmetric positive definite matrix approximation and single pass singular value decomposition and they achieve a better performance than conventional algorithms. Our empirical study also validates the effectiveness and efficiency of our proposed algorithms.