arXiv Machine Learning
Unbounded Characteristic and Universal Kernels
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
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.
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.
arXiv Machine Learning
2d ago
Random Projections for Spectral Algorithms: Optimal Rates in Sobolev Norms
The paper studies random projections (RP) for spectral algorithms, providing a comprehensive analysis of their generalization performance under broad conditions. By exploiting the RKHS embedding property and operator similarity, it establishes optimal learning rates in Sobolev norms that match minimax lower bounds up to logarithmic factors. For common RP implementations—randomized sketches and Nyström sub-sampling—the required projection dimension scales with the effective dimension, reducing computational cost while preserving statistical efficiency.
arXiv Machine Learning
Jun 24
Which Spaces can be Embedded in $L_p$-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
arXiv:2410. 11116v4 Announce Type: replace-cross Abstract: In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces.
arXiv Machine Learning
Sep 1
Signed random Fourier features for fast density estimation with indefinite kernels
arXiv:2608.29265v1 Announce Type: cross Abstract: Kernel density estimation (KDE) is one of the most fundamental statistical estimators of density functions. Its direct implementation on a dataset of...
arXiv Machine Learning
6d ago
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.