Scholarlink

<p>Exclusive Lasso offers significant advantages in scenarios that require sparse solutions within groups, such as multi-omics or gene expression analysis. These applications involve inherent grouping structures where selecting only a subset of variables from each group is crucial due to high correlations among variables within groups. However, a key challenge in optimizing Exclusive Lasso stems from the non-differentiability of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="180_2025_1630_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm within each group. To tackle this issue, we propose a method to transform this norm into a differentiable form using quadratic and sigmoid function approximations. This transformation facilitates the use of a straightforward Newton-based approach to solve the intricate optimization problem. Importantly, our proposed variant of Exclusive Lasso relaxes the strict requirement of selecting at least one variable per group, in contrast to the conventional Exclusive Lasso, and hence enables sparser solutions. Extensive simulation studies underscore the superior performance of our approach compared to both traditional Lasso methods and conventional Exclusive Lasso formulations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Newton-based variant of Exclusive Lasso for improved sparse solutions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月9日

查看全文
  • Dayasri Ravi,
  • Andreas Groll

摘要

Exclusive Lasso offers significant advantages in scenarios that require sparse solutions within groups, such as multi-omics or gene expression analysis. These applications involve inherent grouping structures where selecting only a subset of variables from each group is crucial due to high correlations among variables within groups. However, a key challenge in optimizing Exclusive Lasso stems from the non-differentiability of the \(L_{1}\) L 1 -norm within each group. To tackle this issue, we propose a method to transform this norm into a differentiable form using quadratic and sigmoid function approximations. This transformation facilitates the use of a straightforward Newton-based approach to solve the intricate optimization problem. Importantly, our proposed variant of Exclusive Lasso relaxes the strict requirement of selecting at least one variable per group, in contrast to the conventional Exclusive Lasso, and hence enables sparser solutions. Extensive simulation studies underscore the superior performance of our approach compared to both traditional Lasso methods and conventional Exclusive Lasso formulations.