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<p>Biomedical data often involve a mixture of sparse and non-sparse signals, posing challenges to conventional sparse modeling techniques. This paper presents a novel algorithm, Non-sparse and Sparse Iteration (NSI), designed to jointly estimate sparse and dense components within a unified iterative framework. NSI integrates precision matrix estimation with penalized regression, enabling effective learning from complex feature structures. Theoretical analysis shows that NSI converges to the global minimizer of the joint convex objective solution and achieves optimal rates in terms of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> estimation error. Experimental evaluations on synthetic and real-world datasets demonstrate that NSI outperforms other methods in prediction accuracy, variable selection, and robustness. Application to breast cancer gene expression data reveals consistent selection of clinically relevant genes, demonstrating the method’s practical value in biomedical systems.</p>

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Joint estimation of sparse and dense components through structured iteration

  • 期刊论文

  • 发表日期：

    2025年12月28日

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  • Shun Yu,
  • Yuehan Yang

摘要

Biomedical data often involve a mixture of sparse and non-sparse signals, posing challenges to conventional sparse modeling techniques. This paper presents a novel algorithm, Non-sparse and Sparse Iteration (NSI), designed to jointly estimate sparse and dense components within a unified iterative framework. NSI integrates precision matrix estimation with penalized regression, enabling effective learning from complex feature structures. Theoretical analysis shows that NSI converges to the global minimizer of the joint convex objective solution and achieves optimal rates in terms of \(l_2\) l 2 estimation error. Experimental evaluations on synthetic and real-world datasets demonstrate that NSI outperforms other methods in prediction accuracy, variable selection, and robustness. Application to breast cancer gene expression data reveals consistent selection of clinically relevant genes, demonstrating the method’s practical value in biomedical systems.