# Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling

arXiv: https://arxiv.org/abs/1602.02485 · HTML: https://mlsanity.com/paper/1602.02485/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2016.

## Built on by (most cited first, 18 of 18)

- [Predicting Software Performance with Divide-and-Learn](https://mlsanity.com/paper/2306.06651/) (2023)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Dividable Configuration Performance Learning](https://mlsanity.com/paper/2409.07629/) (2024)
- [Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications](https://mlsanity.com/paper/2306.12670/) (2023)
- [Efficient Model Selection for Predictive Pattern Mining Model by Safe Pattern Pruning](https://mlsanity.com/paper/2306.13561/) (2023)
- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [Distributed Dynamic Safe Screening Algorithms for Sparse Regularization](https://mlsanity.com/paper/2204.10981/) (2022)
- [Distributionally Robust Safe Screening](https://mlsanity.com/paper/2404.16328/) (2024)
- [Safe Screening Rules for Group OWL Models](https://mlsanity.com/paper/2504.03152/) (2025)
- [Safe Distributionally Robust Feature Selection under Covariate Shift](https://mlsanity.com/paper/2603.16062/) (2026)
- [Safe Screening for Sparse Conditional Random Fields](https://mlsanity.com/paper/2111.13958/) (2021)
- [Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant](https://mlsanity.com/paper/2405.17094/) (2024)
- [Distributionally Robust Safe Sample Elimination under Covariate Shift](https://mlsanity.com/paper/2406.05964/) (2024)
- [Generalized Kernel Inducing Points by Duality Gap for Dataset Distillation](https://mlsanity.com/paper/2502.12607/) (2025)
- [Safe Screening Rules for Group SLOPE](https://mlsanity.com/paper/2506.09451/) (2025)
- [Explore and Establish Synergistic Effects Between Weight Pruning and Coreset Selection in Neural Network Training](https://mlsanity.com/paper/2511.09901/) (2025)
- [Gap Safe Screening Rules for Fast Training of Robust Support Vector Machines under Feature Noise](https://mlsanity.com/paper/2603.25221/) (2026)
- [Guarded Block Transfers for Polytope Distance: Linear Convergence with Explicit Constants and Gap-Certified Screening for SVM Training](https://mlsanity.com/paper/2610.15829/) (2026)

## Abstract (arXiv)

The problem of learning a sparse model is conceptually interpreted as the process of identifying active features/samples and then optimizing the model over them. Recently introduced safe screening allows us to identify a part of non-active features/samples. So far, safe screening has been individually studied either for feature screening or for sample screening. In this paper, we introduce a new approach for safely screening features and samples simultaneously by alternatively iterating feature and sample screening steps. A significant advantage of considering them simultaneously rather than individually is that they have a synergy effect in the sense that the results of the previous safe feature screening can be exploited for improving the next safe sample screening performances, and vice-versa. We first theoretically investigate the synergy effect, and then illustrate the practical advantage through intensive numerical experiments for problems with large numbers of features and samples.