Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by identifying saturated coordinates in the course of iterations. This is akin to safe screening techniques previously proposed for sparsity-regularized regression problems. The proposed strategy is provably safe as it provides theoretical guarantees that the identified coordinates are indeed saturated in the optimal solution. Experimental results on synthetic and real data show compelling accelerations for both non-negative and bounded-variable problems.

In this paper, we propose a way to combine two acceleration techniques for the $\ell_1$-regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms, and the use of fast structured approximations of the dictionary matrix. To do so, we introduce a new family of screening tests, termed stable screening, which can cope with approximation errors on the dictionary atoms while keeping the safety of the test (i.e. zero risk of rejecting atoms belonging to the solution support). Some of the main existing screening tests are extended to this new framework. The proposed algorithm consists in using a coarser (but faster) approximation of the dictionary at the initial iterations and then switching to better approximations until eventually adopting the original dictionary. A systematic switching criterion based on the duality gap saturation and the screening ratio is derived.Simulation results show significant reductions in both computational complexity and execution times for a wide range of tested scenarios.