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:2505. 16713v3 Announce Type: replace-cross Abstract: We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument.
By Shogo Nakakita
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:2511. 15615v2 Announce Type: replace-cross Abstract: This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate.
By G\'abor Bal\'azs
In this paper, we study the estimation of a marginal regression function from independent units with repeated binary, count, or continuous responses using ReLU deep neural networks. In the model, we a...
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
arXiv:2609. 25605v1 Announce Type: cross Abstract: In this paper, we study the estimation of a marginal regression function from independent units with repeated binary, count, or continuous responses using ReLU deep neural networks.
By Kexuan Li
arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.
By Swagatam Das, Vaclav Snasel
arXiv:2603. 02043v2 Announce Type: replace Abstract: We revisit transductive learning where predictions are made with the set of all covariates known in advance.
By Jian Qian, Jiachen Xu
arXiv:2609.14802v1 Announce Type: cross
Abstract: Importance weights are essential in domain adaptation under label shift, yet their utility is often undermined by the finite sample uncertainty assoc...
By Mushan Li, Kihyun Han, Yanyuan Ma
The paper investigates Double Machine Learning (DML) estimators under structure‑agnostic (SA) models, which assume the data‑generating law lies within a neighborhood of fixed machine‑learning estimates. It shows that for two of three studied functionals—the quadratic functional in the Gaussian sequence model and the quadratic density integral functional—the DML estimators are asymptotically inadmissible, being dominated by second‑order empirical higher‑order influence function (HOIF) estimators. For the third functional, the expected conditional covariance, both DML and HOIF estimators remain minimax but neither dominates the other.
By Lin Liu, Rajarshi Mukherjee, James M Robins
The paper revisits median‑of‑means estimation from a deterministic optimization perspective, introducing a family of block‑Lp estimators (for 0 < p ≤ 1) that achieve robust learning with heavy‑tailed and adversarially corrupted data. It shows that any convex block M‑estimator cannot attain the trimmed‑block oracle constant, while the nonconvex block‑Lp family provides finite‑sample robustness bounds that approach this oracle constant as p decreases. The authors also prove that the block‑Lp objectives have a benign landscape—every local minimum is close to the true parameter—and combine these results with block‑level concentration to obtain sub‑Gaussian deviation bounds under finite 2+δ moments, extending to high‑dimensional robust mean estimation and sparse regression.
By Angshul Majumdar