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Geometric Kernel Diversity: An Axiomatic Diversity Measure in Euclidean Space
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arXiv Machine Learning
Oct 15
Geometric Kernel Diversity: An Axiomatic Diversity Measure in Euclidean Space
arXiv:2610.19570v1 Announce Type: cross Abstract: Quantifying the diversity of a set of objects is a fundamental problem in machine learning and statistics. Mironov and Prokhorenkova (2025) recently...
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
Jun 18
Fisher Width: A Geometric Measure of Complexity on Statistical Manifolds
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.
arXiv Machine Learning
Sep 15
Low-Dimensional Embeddings for Gaussian Kernels on Manifolds
arXiv:2609.15179v1 Announce Type: cross Abstract: The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian...
arXiv Machine Learning
Sep 17
Sharp margin-based generalization bounds for realizable SVM
arXiv:2609. 17845v1 Announce Type: cross Abstract: Let the exact homogeneous hard-margin support vector machine be trained on \(m\) independent observations from a Borel probability law on a real Hilbert space.
arXiv Machine Learning
Oct 12
Approximating Uniform Random Rotations by Two-Stage Structured Hadamard Rotations in High Dimensions
The paper investigates how well two-stage structured Hadamard rotations approximate uniform random rotations in high-dimensional spaces. It establishes nonasymptotic upper bounds of order √{log d/d} for one-dimensional marginals, while showing a persistent Wasserstein-1 discrepancy for the full vector that does not vanish as dimension grows. These results highlight a separation between marginal and joint approximation quality, though they do not directly translate into algorithmic performance guarantees.