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: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:2510. 25599v2 Announce Type: replace Abstract: Regression tasks, notably in safety-critical domains, require reliable uncertainty quantification, yet the literature remains largely classification-focused.
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: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.
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.
The paper presents a polynomial‑time algorithm for robustly learning Boolean concept classes with respect to a fixed distribution, achieving the optimal error rate of η + ε where η is the noise rate. It builds on Blanc’s earlier, computationally inefficient algorithm and introduces no‑regret learners to overcome the previous limitations. Additionally, the authors provide an efficient method that does not require an ERM oracle for any function class admitting sandwiching polynomials under hypercontractive distributions, including a first polynomial‑time solution for learning halfspaces with Gaussian marginals at error η + ε.
arXiv:2609. 11712v1 Announce Type: cross Abstract: In this paper, we investigate the generalization performance of distributed gradient descent algorithms in a reproducing kernel Hilbert space under a robust loss function $l_{\sigma}$.
The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. It shows that the kernel leads to unrealistically small conditional variances, causing overconfidence in predictive uncertainty, and that this small variance induces numerical ill‑conditioning, necessitating tricks like nugget terms that alter the model. The authors attribute these issues to the kernel’s analytic, highly smooth nature and suggest that analytic stationary kernels in general should be avoided.
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.
The paper introduces a distributionally robust method for learning hyperparameters of first‑order convex optimization algorithms. By minimizing a Wasserstein‑robust performance estimation problem over a dataset of problem instances, the approach interpolates between classical learning‑to‑optimize (L2O) and worst‑case PEP design. The authors solve the resulting problem with stochastic gradient descent, provide high‑probability risk bounds, and demonstrate that the learned algorithms outperform both worst‑case optimal and vanilla L2O baselines on logistic regression, LASSO, and linear programming tasks.
arXiv:2512. 06143v2 Announce Type: replace Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists.