Classification -- Preprocessed and high-dimensional data sets

我们研究了基于不平衡和敏感数据集的两种类型的预处理以及高维特征的结果的分类。众所周知，不平衡的数据集会显著降低分类器在统计学习中的性能。为均衡班级设计的学习算法倾向于偏向多数班级。我们将引入一个理论框架来研究这种偏向多数类的效应，并将与多数类内统计上有效的数据约简预处理联合开发。同时，基于满足局部差分隐私约束的预处理训练数据，研究了监督分类。与{\bf Project~III}合作开发了一个特别具有挑战性的泛函(即无限维)协变量私有化案例。最后，我们将在一个特征变量的数量与样本大小相比不可忽略的框架中调查误分类错误。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。结合项目II，我们研究了迭代梯度下降方法的统计精度，并开发了计算高效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.