Local regression for manifold spatiotemporal processes

A. Torres Signes, M. D. RUIZ MEDINA

Local linear Fréchet regression is extended to the context of Riemannian manifold-valued curve processes. Specifically, a local reformulation of the loss function introduced in Torres-Signes, Frías and Ruiz-Medina (2022) for Fréchet global linear regression for such curve processes is considered. Two approaches are presented, respectively based on computation of the local Fréchet weights in the tangent space, and in the Riemannian manifold. The results in Petersen and Müller (2019) on local linear Fréchet regression are then extended to the context of curve process regression. The asymptotic properties of the proposed local Fréchet predictors are analyzed by simulations.

Petersen, A. and Müller, H.-G. (2019). Fréchet regression for random objects with Euclidean predictors. The Annals of Statistics 49, 691--719.

Torres-Signes, A., Frías, M.P. and Ruiz-Medina M.D. (2022). Multivariate manifold-valued curve regression in time. arXiv:2208.12585.

Keywords: Fréchet regression, Manifold-valued curve processes, Model selection, Riemannian manifold.

GT08.ESPATIEMPO1 Invited Session
November 9, 2023  11:40 AM
CC4: Room 2

A. Medialdea Villanueva, J. M. Angulo Ibáñez, J. Mateu Mahiques, G. Adelfio

I. Fuentes Santos, W. González Manteiga, J. Mateu

T. Goicoa, M. Ugarte, A. Urdangarin Iztueta