arXiv Machine Learning
Sep 25

A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model

The paper establishes nearly quadratic lower bounds for randomized algorithms that perform linear optimization and uniform sampling over convex bodies using a membership oracle. It shows that the lower bound for linear optimization matches the best known upper bound up to a polylogarithmic factor in the dimension, while the bound for uniform sampling improves upon the previous linear lower bound. Additionally, the authors demonstrate that their construction yields the same lower bound for volume estimation.

By Santosh S. Vempala
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 Statistics ML
3d ago

Local polynomial density ratio estimation

arXiv:2609. 38412v1 Announce Type: cross Abstract: We propose a novel local-polynomial estimator of the ratio $r=f/g$ of two $d$-dimensional densities $f$ and $g$, from which independent samples are available.

By Hajo Holzmann, Alexander Meister