arXiv:2603.21144v2 Announce Type: replace
Abstract: This paper proposes a new formulation of functional Gaussian Process regression on manifolds, based on an Empirical Bayes approach, in the spatiote...
By MD Ruiz-Medina, AE Madrid, A Torres-Signes, JM Angulo
arXiv:2510. 21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited.
By Willem Diepeveen, Melanie Weber
The paper develops a nonparametric kernel estimator for tangent vector field regression on a Riemannian manifold without boundary, using parallel transport to align responses before averaging. It derives uniform bias, covariance, and stochastic rates, and constructs a simultaneous confidence tube by whitening the tangent norm into a unit‑variance Gaussian field, whose Gumbel limit yields an explicit intrinsic constant. The method is validated through simulations on various manifolds and applied to reconstruct global wind data, demonstrating spatially varying uncertainty.
By Xiaotian Chang, Yangdi Jiang, Qirui Hu
arXiv:2606. 07926v1 Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
By Kisung You
arXiv:2603.07014v2 Announce Type: replace-cross
Abstract: Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univ...
By Junyoung Park, Irina Gaynanova
The paper introduces an online framework for functional principal component analysis (FPCA) tailored to multidimensional functional data streams. It models functional principal components with tensor product splines, enforcing smoothness and orthonormality via a penalized approach on a Stiefel manifold. The authors present efficient Riemannian stochastic gradient descent and AdaGrad algorithms, along with a dynamic smoothing parameter tuning strategy based on rolling block validation, and provide asymptotic normality results and confidence intervals for the estimators.
By Muye Nanshan, Nan Zhang, Jiguo Cao