Classification -- Preprocessed and high-dimensional data sets

点击翻译按钮获取中文摘要

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.