Wrapped Gaussian Process Functional Regression Model for Batch Data on Riemannian Manifolds

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025. Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and non-linear regression in the context of Euclidean space. However, regression models in non-Euclidean spaces deserve more attention due to the collection of increasing volumes of manifold-valued data. In this context, this paper proposes a concurrent functional regression model for batch data on Riemannian manifolds by estimating both the mean structure and the covariance structure simultaneously. The response variable is assumed to follow a wrapped Gaussian distribution. Nonlinear relationships between manifold-valued response variables and multiple Euclidean covariates can be captured by this model in which the covariates can be functional and/or scalar. The performance of our model has been tested on both simulated and real data, showing that it is an effective and efficient tool to perform functional data regression on Riemannian manifolds.