arXiv Statistics ML
Fourth-Moment Strong Universality for Finite-Type Transpose-Correlated Random Matrices
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arXiv Machine Learning
Jun 2
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
Jun 8
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
Sep 4
Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails
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.
arXiv Machine Learning
Sep 3
Dimension Dependent Correlation Gap Bounds under Restricted Independence
arXiv:2609. 02659v1 Announce Type: cross Abstract: The pairwise independent correlation gap is the ratio of the maximum expected value of a set function under arbitrary dependence to that under pairwise independence, measuring the loss from this independence restriction.
arXiv Machine Learning
Aug 14
Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
arXiv Machine Learning
Sep 17
Accurate Trace Estimation with Fewer Random Bits via Recursive TensorSketch
arXiv:2609. 18577v1 Announce Type: new Abstract: We consider the problem of estimating the trace of an implicit matrix $\mathbf{A} \in \mathbb{R}^{d^p\times d^p}$ that can only be accessed through matrix-vector products queries.