Implicit Manifold Gaussian Process Regression
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this technique to higher dimensions is to leverage the implicit low-dimensional manifold upon which the data actually lies, as postulated by the manifold hypothesis. Prior work ordinarily requires the manifold structure to be explicitly provided though, i.e. given by a mesh or be known to be one of the well-known manifolds like the sphere. In contrast, in this paper we propose a Gaussian process regression technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way. For the resulting model, we discuss its convergence to the Mat\'ern Gaussian process on the assumed manifold. Our technique scales up to hundreds of thousands of data points, and may improve the predictive performance and calibration of the standard Gaussian process regression in high-dimensional settings.
Code (1)
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 ProcessesregressionIntrinsic 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 stru…
regressionTime-adaptive functional Gaussian Process regression
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian mea…
Active Learning for Manifold Gaussian Process Regression
This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method joint…
Active LearningDimensionality ReductionregressionManifold Gaussian Processes for Regression
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are o…
Gaussian Processesregression