# Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach Source: [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach]() Collection index: [llms.txt]() Data updated: 2025-10-26T00:34:23.044Z Authors: Paul Scharnhorst, Emilio T. Maddalena, Yuning Jiang, Colin N. Jones Published: 2021-04-19T19:27:52.000Z ## Abstract The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where outputs are corrupted by bounded measurement noise. The noise can originate from any compactly supported distribution and no independence assumptions are made on the available data. In this setting, we show how computing tight, finite-sample uncertainty bounds amounts to solving parametric quadratically constrained linear programs. Next, properties of our approach are established and its relationship with another methods is studied. Numerical experiments are presented to exemplify how the theory can be applied in a number of scenarios, and to contrast it with other closed-form alternatives. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Dynamics Learning on Quadrotor Example ndata=1000](): Dynamics Learning; Quadrotor Example ndata=1000; Min Suboptimality: 0. - [Dynamics Learning on Quadrotor Example ndata=100](): Dynamics Learning; Quadrotor Example ndata=100; Suboptimality (min): 1. ## Original sources and implementation [Original paper]() [PDF]()