Additive Wrapped Gaussian Process Regression Based on Elastic Net

This paper proposes an intrinsic Additive Wrapped Gaussian Process Regression (AWGPR) model for scenarios where predictors reside in Euclidean space while response variables take values on a Riemannian manifold. By incorporating an additive structure, the proposed model fully captures the intrinsic geometry of the manifold and models the contribution of each feature independently. This design not only effectively handles feature redundancy but also enhances model interpretability. To mitigate the issues of overfitting and instability often associated with single models, we employ an ensemble learning framework to further improve prediction accuracy and robustness. Furthermore, to address potential information redundancy among sub-models, an adaptive aggregation mechanism based on the Elastic Net is developed. The effectiveness of the proposed method is validated through simulation experiments on Riemannian manifolds, including the unit sphere and the space of symmetric positive definite (SPD) matrices. Finally, the model is successfully applied to the task of Diffusion Tensor Imaging (DTI) reconstruction.