Screening Rules for Lasso with Non-Convex Sparse Regularizers
This work addresses efficiency improvements for researchers and practitioners using non-convex Lasso models in high-dimensional data analysis, though it is incremental as it extends existing screening rule concepts to a new context.
The paper tackled the problem of accelerating non-convex Lasso solvers by introducing the first screening rule strategy for non-convex sparse regularizers, resulting in significant computational gains compared to classical methods like coordinate-descent or proximal gradient descent.
Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been proposed in the literature. This work is the first that introduces a screening rule strategy into a non-convex Lasso solver. The approach we propose is based on a iterative majorization-minimization (MM) strategy that includes a screening rule in the inner solver and a condition for propagating screened variables between iterations of MM. In addition to improve efficiency of solvers, we also provide guarantees that the inner solver is able to identify the zeros components of its critical point in finite time. Our experimental analysis illustrates the significant computational gain brought by the new screening rule compared to classical coordinate-descent or proximal gradient descent methods.