arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
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:2607. 02681v1 Announce Type: cross Abstract: Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
arXiv:2601. 16041v2 Announce Type: replace-cross Abstract: In constrained stochastic optimization, one expects that restricting the feasible set, provided it still contains the true parameter, should not increase the statistical risk of the corresponding projection estimator.
arXiv:2601. 18115v2 Announce Type: replace Abstract: We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions.
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
arXiv:2606. 06469v1 Announce Type: cross Abstract: Let $S$ be the set of unit norm linear classifiers $\theta \in \mathbb{R}^d$ which correctly classify every point of a labeled dataset $(X_i,y_i)_{i=1}^n$, $X_i \in \mathbb{R}^d$, $y_i \in \{-1,+1\}$, with a possibly negative margin $\kappa$ fixed in advance.
arXiv:2406. 13944v2 Announce Type: replace-cross Abstract: This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available.
arXiv:2606. 03559v1 Announce Type: new Abstract: For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition.
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.