arXiv:2607. 27532v1 Announce Type: cross Abstract: Heavy tails weaken high-confidence control for the empirical mean.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
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.
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.
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: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...
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.
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.