arXiv Machine Learning
Aug 28

Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences

The monograph explores the relationships between Gaussian processes and reproducing kernel Hilbert spaces (RKHS), two widely used approaches that rely on positive definite kernels. It examines how these frameworks connect and are equivalent across key topics such as regression, interpolation, numerical integration, distributional discrepancies, statistical dependence, and Gaussian process sample path properties. By establishing a unifying perspective based on the equivalence between the Gaussian Hilbert space and the RKHS, the work aims to bridge methods developed independently by the machine learning, statistics, and numerical analysis communities.

By Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, Bharath K. Sriperumbudur
arXiv Machine Learning
Oct 8

Unbounded Characteristic and Universal Kernels

arXiv:2610.09731v1 Announce Type: cross Abstract: Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense su...

By Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o
arXiv Machine Learning
Jul 28

Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD

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 Machine Learning
Jun 11

Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization

arXiv:2606. 11255v1 Announce Type: new Abstract: Bernstein--Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly.

By Taha Bouhsine
arXiv Machine Learning
Oct 19

Measuring Differences between Conditional Distributions using Kernel Embeddings

The paper introduces a unified framework for measuring divergences between conditional distributions using kernel embeddings, termed conditional maximum mean discrepancy (CMMD). It defines a family of CMMD metrics—CMMD_0, CMMD_1, and CMMD_2—each based on different RKHS embeddings, and generalizes them to a level‑s CMMD with clear assumptions and operator‑based smoothing connections. Additionally, the authors present a novel doubly robust estimator for CMMD and demonstrate through experiments that the metric captures complex conditional dependencies for statistical testing.

By Peter Moskvichev, Siu Lun Chau, Dino Sejdinovic