The Lasso has been widely used as a method for variable selection, valued for its simplicity and empirical performance. However, Lasso's selection stability deteriorates in the presence of correlated predictors. Several approaches have been developed to mitigate this limitation. In this paper, we provide a brief review of existing approaches, highlighting their limitations. We then propose a simple technique to improve the selection stability of Lasso by integrating a weighting scheme into the Lasso penalty function, where the weights are defined as an increasing function of a correlation-adjusted ranking that reflects the predictive power of predictors. Empirical evaluations on both simulated and real-world datasets demonstrate the efficacy of the proposed method. Additional numerical results demonstrate the effectiveness of the proposed approach in stabilizing other regularization-based selection methods, indicating its potential as a general-purpose solution.

翻译：Lasso作为一种变量选择方法，因其简洁性和良好的实证性能而得到广泛应用。然而，当存在相关预测变量时，Lasso的选择稳定性会显著下降。目前已有多种方法被提出以缓解这一局限性。本文首先简要回顾现有方法，并指出其不足之处。随后，我们提出一种简单技术，通过在Lasso惩罚函数中引入加权机制来提升其选择稳定性——该权重被定义为基于相关性调整排序的递增函数，该排序反映了预测变量的预测能力。在模拟数据集和真实数据集上的实证评估验证了所提方法的有效性。补充数值实验进一步表明，该方法能有效提升其他基于正则化的选择方法的稳定性，展现了其作为通用解决方案的潜力。