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.
arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.
arXiv:2606. 00413v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response.
The paper studies the numerical solution of the Beurling‑LASSO (BLASSO) for estimating Gaussian mixture models (GMMs) with unknown numbers of components and unknown diagonal covariance matrices. It introduces a Conic Particle Gradient Descent (CPGD) algorithm that incorporates Riemannian gradient descent to respect the Fisher‑Rao geometry of Gaussian distributions. The authors provide theoretical convergence guarantees, including exponential local convergence under a non‑degeneracy condition related to component separation, and demonstrate through numerical experiments that CPGD is more robust to overspecification of components than the EM algorithm.
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...
arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
The paper introduces a pullback Riemannian geometry tailored for multimodal data by employing a latent Gaussian mixture model. It defines a smooth, positive‑definite metric based on responsibility‑weighted component precision, extending the standard single‑Gaussian construction. Experiments on synthetic, multi‑view image, and MNIST datasets demonstrate reduced transport distortion, accurate trajectory recovery, and more realistic interpolation.
arXiv:2505. 05168v4 Announce Type: replace-cross Abstract: Under mild conditions, a least-squares local linear Fr\'echet curve predictor is derived for a response and a regressor evaluated in a separable Hilbert space.
arXiv:2602. 16015v2 Announce Type: replace Abstract: Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces.
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
arXiv:2608.24386v1 Announce Type: cross Abstract: Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. W...
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.