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

arXiv: https://arxiv.org/abs/2109.14171 · HTML: https://mlsanity.com/paper/2109.14171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 68 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process](https://mlsanity.com/paper/1604.03192/) (2016)
- [Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era](https://mlsanity.com/paper/1902.10078/) (2019)
- [Parallelizable sparse inverse formulation Gaussian processes (SpInGP)](https://mlsanity.com/paper/1610.08035/) (2016)
- [Deep State-Space Gaussian Processes](https://mlsanity.com/paper/2008.04733/) (2020)
- [Scalable Gaussian Process Computations Using Hierarchical Matrices](https://mlsanity.com/paper/1808.03215/) (2018)
- [Bayesian functional linear regression with sparse step functions](https://mlsanity.com/paper/1604.08403/) (2016)
- [Bayesian Classification of Multiclass Functional Data](https://mlsanity.com/paper/1808.00662/) (2018)
- [Variational Nonparametric Discriminant Analysis](https://mlsanity.com/paper/1812.03648/) (2018)
- [Bayesian Fusion Estimation via t-Shrinkage](https://mlsanity.com/paper/1812.10594/) (2018)
- [Inverse Ising problem in continuous time: A latent variable approach](https://mlsanity.com/paper/1709.04495/) (2017)
- [Diagonal Discriminant Analysis with Feature Selection for High Dimensional Data](https://mlsanity.com/paper/1807.01422/) (2018)
- [Variational Discriminant Analysis with Variable Selection](https://mlsanity.com/paper/1812.06605/) (2018)

## Built on by (most cited first, 2 of 2)

- [Deep Horseshoe Gaussian Processes](https://mlsanity.com/paper/2403.01737/) (2024)
- [Mixtures of Gaussian Process Experts with SMC2](https://mlsanity.com/paper/2208.12830/) (2022)

## Abstract (arXiv)

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.