Non-stationary Gaussian process discriminant analysis with variable selection for high-dimensional functional data

TL;DR

This paper introduces a unified Gaussian process discriminant analysis method for high-dimensional, non-stationary functional data, effectively combining variable selection and classification with scalable inference and uncertainty quantification.

Contribution

It proposes a novel non-stationary Gaussian process model with an Ising prior, integrating variable selection and classification into a single framework for functional data analysis.

Findings

Effective on simulated datasets

Successful application to proteomics data

Provides explainability and uncertainty quantification

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 non-stationarity. 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 non-stationary 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.