# Refined Gap Safe Screening

This work extends the existing Gap Safe1 screening framework by relaxing global regularity assumptions to their local counterpart. Besides making safe screening possible to a broader class of functions which includes beta-divergences (e.g., the Kullback-Leibler divergence), the proposed approach also improves upon the existing Gap Safe screening rules on previously applicable cases (e.g., logistic regression).

This code corresponds to the following papers:

C.F. Dantas, E. Soubies, C. Févotte, “Expanding boundaries of Gap Safe screening.” Pre-print, 2021.

C.F. Dantas, E. Soubies, C. Févotte, “Safe screening for sparse regression with the Kullback-Leibler divergence.” In ICASSP, 2021.

Related slides here and here

The strong concavity bound $\alpha$ is iteratively refined within the current GAP Safe sphere $\mathcal{B}(\theta,r)$.

1. E. Ndiaye, O. Fercoq, A. Gramfort, and J. Salmon. “Gap safe screening rules for sparsity enforcing penalties.” JMLR, 2017.