The Hessian Screening Rule
This work addresses speed improvements for researchers and practitioners using sparse regression methods, though it appears incremental as it builds on existing screening rule concepts.
The paper tackles the computational challenge of solving sparse regression problems like the lasso by introducing the Hessian Screening Rule, which uses second-order information to discard predictors before model fitting, resulting in outperformance over alternatives on simulated and real datasets with both low and high correlation.
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 $\ell_1$-regularized least-squares (the lasso) and logistic regression. It also performs best in general on the real data sets that we examine.