Nonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data
提出一种结合变量选择与分类的统一框架，用非平稳高斯过程和伊辛先验识别差异分布位置，在乳腺癌和新冠病毒蛋白质组数据上验证了低计算成本、可解释性和不确定性量化。
High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics, and proteomics, the data are often functional in their nature and exhibit a degree of roughness and nonstationarity. These structures pose additional challenges to commonly used methods that rely mainly on a two-stage approach performing variable selection and classification separately. We propose in this work a novel Gaussian process discriminant analysis (GPDA) that combines these steps in a unified framework. Our model is a two-layer nonstationary Gaussian process coupled with an Ising prior to identify differentially-distributed locations. Scalable inference is achieved via developing a variational scheme that exploits advances in the use of sparse inverse covariance matrices. We demonstrate the performance of our methodology on simulated datasets and two proteomics datasets: breast cancer and SARS-CoV-2. Our approach distinguishes itself by offering explainability as well as uncertainty quantification in addition to low computational cost, which are crucial to increase trust and social acceptance of data-driven tools. Supplementary materials for this article are available online.