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:2609. 04822v1 Announce Type: cross Abstract: While diffusion-based methods have recently emerged as effective tools for probing the intrinsic geometry of high-dimensional data, their statistical difficulty remains largely unexplored.
By Jaehee Seo, Wontae Jeong, Jisu Kim
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
By Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
By Vu Khac Ky
arXiv:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.
By Iskander Azangulov, George Deligiannidis, Judith Rousseau
arXiv:2606. 07926v1 Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
By Kisung You
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.
By Tomas Gonzalez, Gonzalo Mena
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
By Hoang-Son Tran, Pranav Gupta, Subhroshekhar Ghosh
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
By Marios Koulakis, Constantin Seibold
arXiv:2606.00661v2 Announce Type: replace-cross
Abstract: Median-of-means (MoM) is a powerful technique that theoretically enables near sub-Gaussian finite-sample rate for parameter estimation when t...
By Nong Minh Hieu, Antoine Ledent
arXiv:2609.36568v1 Announce Type: new
Abstract: Diffusion models have emerged as state-of-the-art generative models, with recent extensions from Euclidean spaces to Riemannian manifolds. However, exi...
By Yuhao Liu, Longbo Huang
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.
By Bing Cheng, Yi-Shuai Niu, Howell Tong, Shing-Tung Yau