# The Hessian Screening Rule

arXiv: https://arxiv.org/abs/2104.13026 · HTML: https://mlsanity.com/paper/2104.13026/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 73 references that are in the map.
- First posted on arXiv 27 Apr 2021.

## Builds on (most cited first, 9 of 9)

- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Celer: a Fast Solver for the Lasso with Dual Extrapolation](https://mlsanity.com/paper/1802.07481/) (2018)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Efficient Smoothed Concomitant Lasso Estimation for High Dimensional Regression](https://mlsanity.com/paper/1606.02702/) (2016)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Hybrid safe-strong rules for efficient optimization in lasso-type problems](https://mlsanity.com/paper/1704.08742/) (2017)
- [ExSIS: Extended Sure Independence Screening for Ultrahigh-dimensional Linear Models](https://mlsanity.com/paper/1708.06077/) (2017)

## Built on by (most cited first, 3 of 3)

- [Continuation Path with Linear Convergence Rate](https://mlsanity.com/paper/2112.05104/) (2021)
- [Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant](https://mlsanity.com/paper/2405.17094/) (2024)
- [Efficient Solvers for SLOPE in R, Python, Julia, and C++](https://mlsanity.com/paper/2511.02430/) (2025)

## Abstract (arXiv)

Predictor screening rules, which discard predictors before fitting a model, have had considerable impact on the speed with which sparse regression problems, such as the lasso, can be solved. In this paper we present a new screening rule for solving the lasso path: the Hessian Screening Rule. The rule uses second-order information from the model to provide both effective screening, particularly in the case of high correlation, as well as accurate warm starts. The proposed rule outperforms all alternatives we study on simulated data sets with both low and high correlation for ℓ1-regularized least-squares (the lasso) and logistic regression. It also performs best in general on the real data sets that we examine.