论文标题
稀疏逻辑回归的加权套索估计：非肿瘤特性带有测量误差
Weighted Lasso Estimates for Sparse Logistic Regression: Non-asymptotic Properties with Measurement Error
论文作者
论文摘要
当我们对高维系统感兴趣并专注于分类性能时，$ \ ell_ {1} $ - 受惩罚的逻辑回归就变得很重要和流行。但是，当不同系数的惩罚均相同并且与数据无关时，LASSO估计可能会出现问题。我们提出了两种类型的加权套索估计，具体取决于McDiarmid不平等的协变量。给定的样本量$ n $和协变量$ p $的尺寸，我们提出的方法的有限样本行为具有不同数量的预测因子，这是通过非质子隔离的甲骨文不等式（例如$ \ ell_ {1} $ - 估计误差和未知参数的平方预测误差）来说明的。我们将方法的性能与对模拟数据的以前的加权估计进行比较，然后应用这些方法进行实际数据分析。
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We proposed two types of weighted Lasso estimates depending on covariates by the McDiarmid inequality. Given sample size $n$ and dimension of covariates $p$, the finite sample behavior of our proposed methods with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as $\ell_{1}$-estimation error and squared prediction error of the unknown parameters. We compare the performance of our methods with former weighted estimates on simulated data, then apply these methods to do real data analysis.
