arXiv:2607. 01895v1 Announce Type: new Abstract: We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix.
arXiv:2608. 02539v1 Announce Type: cross Abstract: We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator.
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
arXiv:2606. 11469v1 Announce Type: cross Abstract: We study the task of density estimation, where we hope to accurately estimate a probability density from $n$ samples.
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. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.
arXiv:2509. 17251v2 Announce Type: replace-cross Abstract: Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems.
arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
arXiv:2607. 21823v1 Announce Type: new Abstract: We show that, up to isotropic scaling, the Gaussian RBF reproducing kernel Hilbert space (RKHS) is asymptotically isometric to Euclidean space in the large bandwidth limit.
arXiv:2607. 00207v1 Announce Type: cross Abstract: We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD).
arXiv:2607. 22931v1 Announce Type: new Abstract: Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches.
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.