For high-dimensional models with a focus on classification performance, the ℓ 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 propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given sample size n and a dimension of covariates p , the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the ℓ 1 -estimation error and the squared prediction error of the unknown parameters. We compare the performance of our method with that of former weighted estimates on simulated data, then apply it to do real data analysis.

中文翻译：

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稀疏逻辑回归的加权套索估计：具有测量误差的非渐近特性

对于关注分类性能的高维模型，ℓ 1 惩罚逻辑回归正变得越来越重要和流行。但是，当不同系数的惩罚都相同且与数据无关时，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，这取决于由 McDiarmid 不等式确定的协变量。给定样本大小 n 和协变量 p 的维度，我们提出的具有不同数量预测变量的方法的有限样本行为由非渐近预言不等式说明，例如 ℓ 1 估计误差和未知参数的平方预测误差. 我们将我们的方法的性能与以前对模拟数据进行加权估计的性能进行比较，然后将其应用于实际数据分析。