Nonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data

ABSTRACT

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.

KEYWORDS:

• Discriminant analysis
• Gaussian process
• High-dimensional analysis
• Nonstationarity
• Variational inference

Supplementary Materials

All supplementary content and codes for this article may be downloaded from the repository: https://github.com/weichangyu10/GPDAPublic.

Notes

1 For ease of notation, we assume the locations $t_1<\cdots <t_T$ are common across all observations, but the discretized model could be extended accordingly.

2 John Hopkins Coronavirus Resource Center https://coronavirus.jhu.edu/

Additional information

Funding

Royal Society of Edinburgh (RSE) Sabbatical Research Grant Holder; this work was supported by the RSE under Grant 69938. This work was supported by the Australian Research Council under grant FT190100374.