# Accelerating Non-Negative and Bounded-Variable Linear Regression Algorithms with Safe Screening

arXiv: https://arxiv.org/abs/2202.07258 · HTML: https://mlsanity.com/paper/2202.07258/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 4 of 4)

- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [On Representer Theorems and Convex Regularization](https://mlsanity.com/paper/1806.09810/) (2018)
- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)
- [Safe squeezing for antisparse coding](https://mlsanity.com/paper/1911.07508/) (2019)

## Abstract (arXiv)

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by identifying saturated coordinates in the course of iterations. This is akin to safe screening techniques previously proposed for sparsity-regularized regression problems. The proposed strategy is provably safe as it provides theoretical guarantees that the identified coordinates are indeed saturated in the optimal solution. Experimental results on synthetic and real data show compelling accelerations for both non-negative and bounded-variable problems.