arXiv:2511. 11498v2 Announce Type: replace-cross Abstract: We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space.
arXiv:2607. 15645v1 Announce Type: cross Abstract: Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers.
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
arXiv:2602. 20971v3 Announce Type: replace-cross Abstract: Bubeck and Selke (2021) propose the connection between the Law of Robustness and robust generalization error as an open problem.
arXiv:2608. 08826v1 Announce Type: new Abstract: Adaptive procedures must work without nuisance information an oracle may use, such as a gradient scale or smoothness index, and robust procedures may have to answer queries whose coordinate and inspection time are chosen only after the data are seen.
arXiv:2603. 28956v2 Announce Type: replace-cross Abstract: The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural networks.
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
arXiv:2607. 24732v1 Announce Type: cross Abstract: Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples.
arXiv:2405. 11454v3 Announce Type: replace Abstract: We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value.
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
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:2202. 08832v3 Announce Type: replace-cross Abstract: We study a general class of optimization problems with decision variable $\boldsymbol{\Theta} \in \mathbb{R}^{p \times k}$ and cost function which is the sum of $n$ terms, each dependent on $\boldsymbol{\Theta}$ through the $k$-dimensional projection $\boldsymbol{\Theta}^\top \boldsymbol{x}_i$, where $\boldsymbol{x}_i$, $i \leq n$ are i.
arXiv:2503. 04712v3 Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods.