The paper introduces MiNCE, a nonparametric framework for constructing minimum‑norm confidence envelopes that provide nonasymptotic, simultaneous confidence regions for band‑limited functions using Reproducing Kernel Hilbert Spaces. It proves strong uniform consistency of these envelopes for both noise‑free and noisy data under mild noise assumptions, and extends the results to the frequency domain to yield consistent confidence bands for smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation confirm the theoretical findings, showing the envelopes contract toward the target function as sample size grows.
We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.
arXiv:1812.09632v3 Announce Type: replace Abstract: We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributi...
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.
The monograph explores the relationships between Gaussian processes and reproducing kernel Hilbert spaces (RKHS), two widely used approaches that rely on positive definite kernels. It examines how these frameworks connect and are equivalent across key topics such as regression, interpolation, numerical integration, distributional discrepancies, statistical dependence, and Gaussian process sample path properties. By establishing a unifying perspective based on the equivalence between the Gaussian Hilbert space and the RKHS, the work aims to bridge methods developed independently by the machine learning, statistics, and numerical analysis communities.
arXiv:2609.15785v1 Announce Type: cross Abstract: We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional...
arXiv:2312. 15341v1 Announce Type: cross Abstract: We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems.
arXiv:2504.18184v5 Announce Type: replace Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
arXiv:2609.08671v1 Announce Type: cross Abstract: In this paper, we consider the scalar-on-function linear regression model under a realistic sampling scheme in which the functional covariates are ob...
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
arXiv:2603. 16481v3 Announce Type: replace Abstract: Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control.
arXiv:2601. 13102v3 Announce Type: replace-cross Abstract: Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators.
arXiv:2607. 27995v1 Announce Type: cross Abstract: Adversarial training has emerged as a powerful approach for protecting models against adversarial attacks in a broad range of real-world applications.