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.
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:2607. 27532v1 Announce Type: cross Abstract: Heavy tails weaken high-confidence control for the empirical mean.
arXiv:2512. 13997v2 Announce Type: replace-cross Abstract: Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions.
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: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: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. 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.
arXiv:2609.38875v1 Announce Type: cross Abstract: This paper develops a framework for estimation and inference on the volumes of sets that are projections of critical function sets, focusing particul...
arXiv:2505. 14251v2 Announce Type: replace Abstract: We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data.
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.
The paper introduces MiNCE, a nonparametric framework for constructing minimum‑norm confidence envelopes that provide nonasymptotic, simultaneous confidence regions for band‑limited functions using Reproducing Kernel Hilbert Spaces. It proves strong uniform consistency of these envelopes for both noise‑free and noisy data under mild noise assumptions, and extends the results to the frequency domain to yield consistent confidence bands for smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation confirm the theoretical findings, showing the envelopes contract toward the target function as sample size grows.
arXiv:2409. 09903v3 Announce Type: replace-cross Abstract: Softmax Mixture Models (SMMs) are discrete $K$-component mixture models for the probabilities of selecting one of $p$ candidate feature vectors $X_1,\ldots,X_p\in\mathbb{R}^L$ in heterogeneous populations and are widely used in econometrics and scientific applications.