Chen Xingyu, Yang Yuehan
School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China.
Stat Methods Med Res. 2023 Jun;32(6):1145-1158. doi: 10.1177/09622802231163335. Epub 2023 Mar 28.
Highly correlated structures appear in various fields, such as biology, biochemistry, and finance, with challenges of dimensionality and sparse estimation. To solve this problem, we propose an algorithm called local linear approximation with the Laplacian smoothing penalty (LLA-LSP). This method produces an accurate and smooth estimate that incorporates the correlation structure among predictors. We compare and discuss the difference between the Laplacian smoothing penalty and the total variance penalty. We prove that this algorithm converges to the oracle solution in a few iterations with a large probability. Numerical results show that the LLA-LSP has good performance in both variable selection and estimation. We apply the proposed algorithm to two biological datasets, a gene expression dataset and a chemical protein dataset, and provide meaningful insights.
高度相关的结构出现在各个领域，如生物学、生物化学和金融领域，存在维度和稀疏估计方面的挑战。为了解决这个问题，我们提出了一种名为带拉普拉斯平滑惩罚的局部线性近似（LLA-LSP）的算法。该方法产生一个准确且平滑的估计，它纳入了预测变量之间的相关结构。我们比较并讨论了拉普拉斯平滑惩罚和总方差惩罚之间的差异。我们证明该算法在几次迭代中大概率收敛到神谕解。数值结果表明LLA-LSP在变量选择和估计方面都具有良好的性能。我们将所提出的算法应用于两个生物学数据集，一个基因表达数据集和一个化学蛋白质数据集，并提供了有意义的见解。
