arXiv Statistics ML
Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator
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Adam under Generalized Smoothness with Second-Moment-Type Stochastic Gradients
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 Machine Learning
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Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
arXiv Machine Learning
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How Accurately Can a Gaussian Approximate Stochastic Approximation Iterates?
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv Machine Learning
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Counterexamples and Sufficient Conditions: Comments on "Optimally-Transported Generalized Method of Moments"
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 Machine Learning
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Statistical Inference for Stochastic Gradient Descent: Beyond Finite Variance
arXiv:2605. 26000v2 Announce Type: replace-cross Abstract: Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization.
arXiv AI
Sep 3
Nonasymptotic CLT and Error Bounds for Linear Two-Time-Scale Stochastic Approximation
arXiv:2502. 09884v4 Announce Type: replace-cross Abstract: We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise.