arXiv Machine Learning
Jun 2

On Median of Incomplete U-Statistics

arXiv:2606. 00661v1 Announce Type: cross Abstract: We establish the finite-sample concentration rate for the Median-of-Incomplete-U-Statistics (MIU), an efficient robust estimator for the expectation of symmetric kernels.

By Nong Minh Hieu
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
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.

By Tomer Zilca, Gal Mendelson
arXiv Machine Learning
Oct 7

Sample-Optimal Estimation of the Fr\'echet Inception Distance

The paper investigates the sample complexity of estimating the Fréchet Inception Distance (FID) between high‑dimensional Gaussian distributions when one distribution is known. It establishes tight bias and variance bounds for the empirical plug‑in estimator, shows how higher‑order extrapolation reduces bias, and introduces a new Relative Taylor Debiasing (RTD) algorithm that achieves optimal sample complexity. Experiments on synthetic data and ImageNet confirm the theoretical predictions and demonstrate RTD’s superior accuracy with limited samples.

By Ziyun Chen, Jerry Li, Kevin Tian, Yusong Zhu