arXiv:2606. 00322v1 Announce Type: new Abstract: We introduce a perturbative approach for nonparametric instrumental variable (NPIV) estimation.
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:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
arXiv:2608. 07281v1 Announce Type: cross Abstract: This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally.
arXiv:2609.09211v1 Announce Type: new Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
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:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.
arXiv:2608. 04860v1 Announce Type: cross Abstract: This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target population.
arXiv:2609. 18901v1 Announce Type: cross Abstract: In physics-informed machine learning, a target function $u^*$ is learned from noisy value observations $y_i=u^*(x_i)+ \varepsilon_i$, together with differential information, given either by noisy observations $d_j=(Du^*)(z_j)+\xi_j$ or by a known physical constraint $Du^*=v$.
arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.
arXiv:2609.38565v1 Announce Type: new Abstract: Over the past 25 years, sketching and sampling have become widely used tools for accelerating large-scale regression. In iterative randomized solvers,...
arXiv:2510.02532v2 Announce Type: replace-cross Abstract: Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensio...