# Safe squeezing for antisparse coding

arXiv: https://arxiv.org/abs/1911.07508 · HTML: https://mlsanity.com/paper/1911.07508/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material](https://mlsanity.com/paper/2203.00987/) (2022)
- [One to beat them all: "RYU" -- a unifying framework for the construction of safe balls](https://mlsanity.com/paper/2312.00640/) (2023)
- [Iterative regularization for low complexity regularizers](https://mlsanity.com/paper/2202.00420/) (2022)
- [Accelerating Non-Negative and Bounded-Variable Linear Regression Algorithms with Safe Screening](https://mlsanity.com/paper/2202.07258/) (2022)

## Abstract (arXiv)

Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex program involving an ℓ_∞-norm penalty combined with a quadratic discrepancy. In this paper, we propose a new methodology, dubbed safe squeezing, to accelerate the computation of antisparse representation. We describe a test that allows to detect saturated entries in the solution of the optimization problem. The contribution of these entries is compacted into a single vector, thus operating a form of dimensionality reduction. We propose two algorithms to solve the resulting lower dimensional problem. Numerical experiments show the effectiveness of the proposed method to detect the saturated components of the solution and illustrates the induced computational gains in the resolution of the antisparse problem.