arXiv:2609.37787v1 Announce Type: new Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
The paper critiques the optimally‑transported generalized method of moments (OTGMM) estimator introduced by Schennach & Starck (2026a), presenting counterexamples that invalidate Theorems 2–6 under their stated assumptions. It shows that the small‑error assumptions fail to guarantee consistency and asymptotic normality, and that the large‑error analysis leads to a modified‑moment GMM estimator that can diverge from the true OTGMM minimizer, even in simple scalar and overidentified models. The authors further provide a sufficient condition ensuring that solutions of the modified moment equations also solve the original constrained problem, and replace a problematic Assumption 16 with a matrix condition that restores the required bound.
arXiv:2605. 26000v2 Announce Type: replace-cross Abstract: Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization.
arXiv:2502. 09884v4 Announce Type: replace-cross Abstract: We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise.
The paper investigates preference elicitation under the Bradley‑Terry‑Luce model, focusing on estimating an unknown partworth vector from pairwise queries that satisfy a joint identifiability condition. It derives minimax lower bounds and shows that the canonical maximum likelihood estimator (MLE) exists, is unique, and achieves near‑optimal error rates once the sample size exceeds a design‑dependent threshold, without requiring compactness constraints or external regularizers. The analysis decomposes the estimation error into a linear stochastic term, a second‑order bias, and a higher‑order remainder, providing a unified non‑asymptotic theory for parametric utility elicitation.
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.
arXiv:2508.06483v3 Announce Type: replace-cross Abstract: We study the self-normalized concentration of vector-valued stochastic processes. We focus on bounds for "sub-$\psi$" processes, a well-known...
arXiv:2606. 19876v1 Announce Type: new Abstract: The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems.
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.