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

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.

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

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 lsing 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.

Novel semi-metrics for multivariate change point analysis and anomaly detection.

This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, by measuring distances between structural breaks within such a collection. We introduce a class of semi-metric distance measures, which we term MJ distances. These semi-metrics provide an advantage over existing options such as the Hausdorff and Wasserstein metrics. We prove they have desirable properties, including better sensitivity to outliers, while experiments on simulated data demonstrate that they uncover similarity within collections of time series more effectively. Semi-metrics carry a potential disadvantage: without the triangle inequality, they may not satisfy a "transitivity property of closeness." We analyse this failure with proof and introduce an computational method to investigate, in which we demonstrate that our semi-metrics violate transitivity infrequently and mildly. Finally, we apply our methods to cryptocurrency and measles data, introducing a judicious application of eigenvalue analysis.