# Safe Screening With Variational Inequalities and Its Application to LASSO

arXiv: https://arxiv.org/abs/1307.7577 · HTML: https://mlsanity.com/paper/1307.7577/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2013.

## Built on by (most cited first, 11 of 11)

- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Safe Screening for Logistic Regression with ℓ0-ℓ2 Regularization](https://mlsanity.com/paper/2202.00467/) (2022)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications](https://mlsanity.com/paper/2306.12670/) (2023)
- [Screening for Sparse Online Learning](https://mlsanity.com/paper/2101.06982/) (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)
- [Safe Distributionally Robust Feature Selection under Covariate Shift](https://mlsanity.com/paper/2603.16062/) (2026)
- [Screening for a Reweighted Penalized Conditional Gradient Method](https://mlsanity.com/paper/2107.01106/) (2021)
- [Safe Screening for Unbalanced Optimal Transport](https://mlsanity.com/paper/2307.00247/) (2023)

## Abstract (arXiv)

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for a certain value of the regularization parameter, is a technique for improving the computational efficiency. Safe screening is gaining increasing attention since 1) solving sparse learning formulations usually has a high computational cost especially when the number of features is large and 2) one needs to try several regularization parameters to select a suitable model. In this paper, we propose an approach called "Sasvi" (Safe screening with variational inequalities). Sasvi makes use of the variational inequality that provides the sufficient and necessary optimality condition for the dual problem. Several existing approaches for Lasso screening can be casted as relaxed versions of the proposed Sasvi, thus Sasvi provides a stronger safe screening rule. We further study the monotone properties of Sasvi for Lasso, based on which a sure removal regularization parameter can be identified for each feature. Experimental results on both synthetic and real data sets are reported to demonstrate the effectiveness of the proposed Sasvi for Lasso screening.