Classification -- Preprocessed and high-dimensional data sets

我们研究分类的基础上设计的不平衡和敏感的数据集，以及高维特征的后果的两种类型的预处理。已知不平衡数据集会显著降低统计学习中分类器的性能。为均衡类设计的学习算法往往偏向于多数类。 我们将引入一个理论框架来研究这种偏向多数类效应，并将与多数类中统计有效的数据缩减预处理共同开发。在并行，监督分类研究基于预处理的训练数据满足$\alpha$-局部差分隐私约束。特别具有挑战性的私有化功能案例（即，无限维）协变量是与{\bf Project~III}合作开发的。 最后，我们将调查的误分类错误的框架中的特征变量的数量是不可忽略的样本量相比。在高维特征的情况下，经典统计过程的计算成本变得令人望而却步。我们与{\bf Project~II}一起研究迭代梯度下降方法的统计精度，并开发计算效率高且完全数据驱动的学习算法。

We study classification based on two types of preprocessing designed for imbalanced and sensitive data sets, as well as consequences of high dimensional features. Imbalanced data sets are known to significantly reduce the performance of classifiers in statistical learning. Learning algorithms designed for equally balanced classes tend to be biased towards the majority class. We will introduce a theoretical framework to study this bias-towards-the-majority-class effect and will develop jointly with {\bf Project~IV} statistically efficient data reduction preprocessing within the majority class. In parallel, supervised classification is studied based on preprocessed training data satisfying an $\alpha$-local differential privacy constraint. The particularly challenging case of privatized functional (i.e., infinite dimensional) covariates is developed in collaboration with {\bf Project~III}. Finally, we will investigate the misclassification error in a framework where the number of feature variables is not negligible compared to sample size. In the case of high-dimensional features the computational cost of classical statistical procedures becomes prohibitive. Together with {\bf Project~II} we investigate the statistical accuracy of iterative gradient descent methods and develop computationally efficient and fully data driven learning algorithms.