2021/10/14 by Théo Guyard, Guyard, Théo, Cédric Herzet +3
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Electrical engineering #Machine Learning and Algorithms #Multi-Criteria Decision Making #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2110.07308
openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost. Our work leverages the concept of safe screening, well known for sparsity-inducing convex problems, and some recent advances in this field for l0-penalized regression problems.