Intrinsic Wrapped Gaussian Process Regression Modeling for Manifold-valued Response Variable
In this paper, we propose a novel intrinsic wrapped Gaussian process regression model for response variable measured on Riemannian manifold. We apply the parallel transport operator to define an intrinsic covariance structure addressing a critical aspect of constructing a well defined Gaussian process regression model. We show that the posterior distribution of regression function is invariant to the choice of orthonormal frames for the coordinate representations of the covariance function. This method can be applied to data situated not only on Euclidean submanifolds but also on manifolds without a natural ambient space. The asymptotic properties for estimating the posterior distribution is established. Numerical studies, including simulation and real-world examples, indicate that the proposed method delivers strong performance.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Wrapped Gaussian Process Regression on Riemannian Manifolds
Gaussian process (GP) regression is a powerful tool in non-parametric regression providing uncertainty estimates. However, it is limited to data in vector spaces. In fields such as shape analysis and diffusion tensor ima…
Gaussian ProcessesregressionCombining additivity and active subspaces for high-dimensional Gaussian process modeling
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they …
Gaussian ProcessesUncertainty QuantificationIntrinsic Non-stationary Covariance Function for Climate Modeling
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stat…
regressionActive Learning for Gaussian Process Considering Uncertainties with Application to Shape Control of Composite Fuselage
In the machine learning domain, active learning is an iterative data selection algorithm for maximizing information acquisition and improving model performance with limited training samples. It is very useful, especially…
Active LearningregressionTowards Variational Flow Matching on General Geometries
We introduce Riemannian Gaussian Variational Flow Matching (RG-VFM), an extension of Variational Flow Matching (VFM) that leverages Riemannian Gaussian distributions for generative modeling on structured manifolds. We de…