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

arXiv: https://arxiv.org/abs/2409.03181 · HTML: https://mlsanity.com/paper/2409.03181/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2024.

## Built on by (most cited first, 3 of 3)

- [Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2502.01512/) (2025)
- [Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variable](https://mlsanity.com/paper/2411.18989/) (2024)
- [Rolled Gaussian process models for curves on manifolds](https://mlsanity.com/paper/2503.21980/) (2025)

## Abstract (arXiv)

Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean spaces deserve more attention due to 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 mean structure and covariance structure simultaneously. The response variable is assumed to follow a wrapped Gaussian process 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 data and real data, showing it is an effective and efficient tool in conducting functional data regression on Riemannian manifolds.