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
arXiv:2201. 01973v3 Announce Type: replace-cross Abstract: The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks.
By Saptarshi Chakraborty, Debolina Paul, Swagatam Das
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:2606.00661v2 Announce Type: replace-cross
Abstract: Median-of-means (MoM) is a powerful technique that theoretically enables near sub-Gaussian finite-sample rate for parameter estimation when t...
By Nong Minh Hieu, Antoine Ledent
arXiv:2603. 16798v2 Announce Type: replace Abstract: We study mean estimation for a Gaussian distribution with identity covariance in $\mathbb{R}^d$ under a missing data scheme termed realizable $\epsilon$-contamination model.
By Ilias Diakonikolas, Daniel M. Kane, Thanasis Pittas
The paper proposes methods for estimating many high‑dimensional mean vectors from independent samples by forming convex combinations of empirical means. Two data‑dependent weighting strategies are introduced: one uses a testing procedure to pick low‑variance neighbouring means, yielding a closed‑form plug‑in formula; the other minimizes an upper confidence bound on quadratic risk. Theoretical results show these approaches asymptotically achieve oracle (minimax) risk improvements as the effective dimension grows, and experiments confirm their effectiveness on simulated and real kernel mean embedding tasks.
By Gilles Blanchard (LMO, DATASHAPE), Jean-Baptiste Fermanian (LMO), Hannah Marienwald (TUB)
arXiv:2609. 20749v1 Announce Type: cross Abstract: Location estimation exhibits markedly different finite-sample behavior across noise distributions: regular families typically yield root-\(n\) rates, whereas compactly supported laws may admit faster, boundary-driven rates.
By Qiaosen Wang, Chao Gao
The paper tackles two key gaps in streaming PCA using Oja's algorithm: it establishes sharp operator‑norm convergence for general‑rank subspaces under sub‑Gaussian data, and it provides distributional inference for the resulting subspace estimator. The authors remove non‑vanishing remainder terms from existing analyses, achieving rates that match minimax bounds in both dense‑tail and sparse‑tail regimes. They further develop a linearization of Oja’s iterates, enabling high‑dimensional Gaussian approximations and an online multiplier bootstrap for practical inference.
By Haoshu Xu, Hongzhe Li
arXiv:2607. 20119v1 Announce Type: cross Abstract: We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts.
By Shijie Zhong, Jiangfeng Fu
arXiv:2603. 11308v3 Announce Type: replace Abstract: Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.
By Mario Sayde, Christopher Khater, Jihad Fahs, Ibrahim Abou-Faycal
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
The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
By Shi Fu, Huibo Xu, Qixin Zhang, Dacheng Tao