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<p>This paper addresses the challenge of low-rank matrix estimation in high-dimensional settings, where the dimensions of the matrix far exceed the sample size. To overcome this, we propose a novel approach that integrates sparsity and nonconvex regularization. Our method employs nonconvex penalties, such as the smoothly clipped absolute deviation (SCAD) and the minimax concave penalty (MCP), to reduce estimation bias and improve convergence rates. We develop efficient optimization algorithms to handle the resulting complex problems. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate the robustness and effectiveness of our approach in various high-dimensional contexts.</p>

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Simultaneously sparse and low-rank matrix estimation via \(l_1\)-norm and nonconvex regularization

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Ling Peng,
  • Shanshan Tang,
  • Fei Huang,
  • Weiying Ping

摘要

This paper addresses the challenge of low-rank matrix estimation in high-dimensional settings, where the dimensions of the matrix far exceed the sample size. To overcome this, we propose a novel approach that integrates sparsity and nonconvex regularization. Our method employs nonconvex penalties, such as the smoothly clipped absolute deviation (SCAD) and the minimax concave penalty (MCP), to reduce estimation bias and improve convergence rates. We develop efficient optimization algorithms to handle the resulting complex problems. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate the robustness and effectiveness of our approach in various high-dimensional contexts.