The paper studies distributional drift in nonstationary weighted risk minimization by breaking down excess risk into estimation, drift, and approximation parts. It argues that traditional discrepancy-based bounds are often overly conservative because they can scale larger than the actual excess-risk contribution and react to risk surface changes that do not affect the optimal predictor. The authors provide a tighter oracle drift bound, analyze its behavior in parametrized regression models—particularly linear regression—and extend the results to nonparametric regression.
By Tobias Brock, Thomas Nagler
arXiv:2505.24843v3 Announce Type: replace
Abstract: Predictors often exploit spurious correlations that fail under distribution shift, undermining out-of-distribution (OOD) robustness. Invariant pair...
By Ruqi Bai, Easton Currie, Yao Ji, Mingyu Kim, Zeyu Zhou, David I. Inouye
The paper investigates weighted empirical risk minimization under nonstationary data, decomposing the excess risk into a learning component and a drift component. It establishes oracle inequalities for the learning error under mixing conditions, uniformly over arbitrary weight classes, and derives explicit bounds for drift errors in square loss settings, covering structural‑break and smoothly drifting processes. The analysis is extended to auto‑regression problems with linear models, basis approximations, and neural networks, revealing that optimal weights balance learning and drift via a bias–variance trade‑off and recover minimax‑optimal rates in unweighted, stationary cases.
By Tobias Brock, Thomas Nagler
arXiv:2606. 00857v1 Announce Type: cross Abstract: Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving.
By Xinyi Ning, Zilin Bian, Dachuan Zuo, Semiha Ergan, Kaan Ozbay
arXiv:2607. 05536v1 Announce Type: cross Abstract: Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers.
By Jie Zhang, Natalie Frank
arXiv:2610.07637v1 Announce Type: cross
Abstract: Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture thi...
By Kaito Takanami, Takashi Takahashi, Yoshiyuki Kabashima