Discriminant Analysis in High-Dimensional Latent Factor Models

该研究项目涉及高维特征的分类，这是统计学习理论的重要组成部分。该项目将制定具有低维隐藏结构的高维潜在因素模型，以保证基于高维数据的适当预测的成功统计分类性能。这项研究的结果，预计将促进了解如何实现最佳分类。该项目对免疫学和癌症研究的最新进展有重要的应用，这些研究揭示了隐藏的机制可以直接与健康结果联系起来。该项目提供了一种分析这种高维数据集的原则性方法，并将提供计算效率高的分类规则。该项目将与计算生物学家合作，以验证新的模型和方法。具体而言，该项目将构建基于主成分分析的新型分类器，其中必要的去偏部分随后是线性判别分析，并开发其统计和计算特性。这个项目的重点是研究的重要子类的无调谐分类器，插值的数据，但仍然具有良好的预测能力。此外，本研究的目的是开发minimax自适应边界的过度误分类错误下一般潜在因素模型的规格，并证明新的方法实现这些界限，从而建立他们的速率最优。最后，新技术的实用性将通过应用于免疫学数据来证明。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project concerns classification of high-dimensional features, an important part of statistical learning theory. The project will formulate high-dimensional latent factor models that have a low-dimensional, hidden structure to guarantee successful statistical classification performance based on suitable projections of the high-dimensional data. Results of this research are expected to advance understanding on how to achieve optimal classification. This project has important applications to recent advances in immunology and cancer studies, which revealed that hidden mechanisms can be directly connected to health outcomes. This project offers a principled way to analyze such high-dimensional datasets and will provide computationally efficient classification rules. The project will involve collaboration with computational biologists to validate the new models and methodology.Specifically, this project constructs novel classifiers based on principal component analysis with a necessary debiasing part followed by linear discriminant analysis and develops their statistical and computational properties. This project focuses on study of the important subclass of tuning-free classifiers that interpolate the data, but still possess good predictive power. In addition, this research aims to develop minimax adaptive bounds for the excess misclassification error under general latent factor model specifications and to prove that the new methods achieve these bounds, thereby establishing their rate optimality. Finally, the usefulness of the new techniques will be demonstrated via applications to data from immunology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.