Efficient Screening-Based Optimization: A Greedy Approach for Large-Scale Sparse Learning

This paper proposes Efficient Screening-Based Optimization (ESO), a dual-threshold greedy screening framework for large-scale sparse learning. ESO integrates adaptive feature evaluation with dynamic parameter updates to address computational inefficiency in ultra-sparse scenarios. By employing a probabilistic screening mechanism and prox-based test functions, it achieves 50-70% faster computation than state-of-the-art methods when regularization parameters approach 105. Experiments on synthetic and real-world datasets demonstrate robustness across penalty functions (L1, SCAD, MCP) and data types (image, genomic). Theoretical analysis confirms solution consistency, while parameter sensitivity studies guide practical implementation. The method significantly enhances scalability for high-dimensional problems.