B1485
Title: Wrapped Gaussian process functional regression for batch data on Riemannian manifolds
Authors: Jinzhao Liu - Newcastle University (United Kingdom) [presenting]
Jian Qing Shi - Southern Univesity of Science and Technology (China)
Abstract: Regression is an essential and fundamental methodology in statistical analysis. Plenty of literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean spaces deserve more attention since people observed enormous manifold-valued data. Most existing regression models are nonviable in such a setup due to the lack of global vector space structure. Taking the advantage of massive manifold-valued data, we propose a concurrent functional regression model for batch data on a Riemannian manifold by estimating both mean structure and covariance structure simultaneously. The response variable is considered as a wrapped Gaussian process functional regression model. Nonlinear relationship between manifold-valued response variables and multiple Euclideancovariates can be captured by this model in which the covariates could be functional and scalar. The performance of our model has been tested on both generated data and real data, which endorses it as an effective and efficient tool in conducting functional data regression on a Riemannian manifold.
