2023/10/12 by Alejandro Cholaquidis, Fabrice Gamboa, Cholaquidis, Alejandro +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Computer and information sciences #Genetic and phenotypic traits in livestock #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Morphological variations and asymmetry #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2310.08209
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in the space of covariance matrices, data on the Grassmannian manifold obtained as a result of principal component analysis, among many others. In this work we investigate prediction sets for regression scenarios when the response variable, denoted by Y, resides in a manifold, and the covariable, denoted by X, lies in an Euclidean space. This extends the concepts delineated in \citewaser14 to this novel context. Aligning with traditional principles in conformal inference, these prediction sets are distribution-free, indicating that no specific assumptions are imposed on the joint distribution of (X,Y), and they maintain a non-parametric character. We prove the asymptotic almost sure convergence of the empirical version of these regions on the manifold to their population counterparts. The efficiency of this method is shown through a comprehensive simulation study and an analysis involving real-world data.