← Back to all news
arXiv Machine Learning By Xiaotian Chang, Yangdi Jiang, Qirui Hu

Riemannian Simultaneous Inference for Tangent Vector Field Regression

Read the original on arXiv Machine Learning →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Jul 14

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds

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.

By Swagatam Das, Vaclav Snasel
safety
More like this →
arXiv Statistics ML
Sep 25

Riemannian Gradient Descent for Gaussian Mixture Models with unknown diagonal covariances

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.

By Romane Giard, Yohann De Castro, Roland Denis, Cl\'ement Marteau
efficiency
More like this →
arXiv Machine Learning
1d ago

Beyond Unimodal Bases: Pullback Geometry for Multimodal Data

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.

By Honglei Brinkmann, Lucas Ng, Georgios Batzolis, Mark Girolami, Carola-Bibiane Sch\"onlieb, Willem Diepeveen
multimodal
More like this →