Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Optimal kernel regression bounds under energy-bounded noise
Authors: Amon Lahr, Johannes Köhler, Anna Scampicchio, Melanie N. Zeilinger
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical comparison In this experiment, the size of the uncertainty regions is compared. Using a squared-exponential kernel kf(x, x ) = exp( x x 2/ℓ2), ℓ= 1, for the latent function, as well as a Dirac noise kernel kw(x, x ) = δ(x x ) on the domain X = [0, 4], random latent functions are generated with f tr 2 Hkf = Γ2 f = 1. Training data are sampled based on measurement noise following a zero-mean truncated Gaussian distribution with standard deviation and bounded absolute value equal to ϵ = 0.01, which is R-sub-Gaussian for R = ϵ. The corresponding noise-energy bound is derived as Γ2 w = Nϵ2. We compare the proposed bound (Theorem 1), which is optimal given only the information wtr 2 Hkw Γ2 w, the relaxed bound (Lemma 1) with σ = ϵ, and a standard high-probability error bound [Abbasi-Yadkori, 2013], cf. [Fiedler et al., 2024, Eq. (7)], which uses only sub-Gaussianity of the noise and provides a valid bound with probability p = 0.99, similar to [Srinivas et al., 2012; Fiedler et al., 2021]. Optimality of the numerical solution to (9) is guaranteed by solving a convex reformulation of (2) (see Appendix A) using CVXPY [Diamond and Boyd, 2016; Agrawal et al., 2018]. Figure 2 compares the area of the uncertainty region for N = 1, . . . , 103 randomly sampled training points, averaged over 103 runs for randomly sampled latent functions f tr. |
| Researcher Affiliation | Academia | Amon Lahr ETH Zurich EMAIL Johannes Köhler ETH Zurich EMAIL Anna Scampicchio ETH Zurich EMAIL Melanie N. Zeilinger ETH Zurich EMAIL |
| Pseudocode | No | The paper describes methods through mathematical derivations and problem formulations (e.g., optimization problem (2) and (4)) but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code to reproduce the experiments is publicly available at https://gitlab.ethz.ch/ics/ bounded-energy-rkhs-bounds and at https://doi.org/10.3929/ethz-c-000785083. |
| Open Datasets | No | random latent functions are generated with f tr 2 Hkf = Γ2 f = 1. Training data are sampled based on measurement noise following a zero-mean truncated Gaussian distribution with standard deviation and bounded absolute value equal to ϵ = 0.01, which is R-sub-Gaussian for R = ϵ. |
| Dataset Splits | No | random latent functions are generated with f tr 2 Hkf = Γ2 f = 1. Training data are sampled based on measurement noise following a zero-mean truncated Gaussian distribution with standard deviation and bounded absolute value equal to ϵ = 0.01... Figure 2 compares the area of the uncertainty region for N = 1, . . . , 103 randomly sampled training points, averaged over 103 runs for randomly sampled latent functions f tr. Fig. 3 shows the success rate in terms of the share of feasible problems for an increasing amount of training data on a grid of 500 test points in the domain x(k) [ 2, 2], repeated 20 times with random noise realizations. |
| Hardware Specification | Yes | The optimization problems are implemented in Cas ADi [Andersson et al., 2019] and solved using the interior-point optimizer IPOPT [Wächter and Biegler, 2006] on an Intel i9-7940X CPU. |
| Software Dependencies | No | Optimality of the numerical solution to (9) is guaranteed by solving a convex reformulation of (2) (see Appendix A) using CVXPY [Diamond and Boyd, 2016; Agrawal et al., 2018]. The optimization problems are implemented in Cas ADi [Andersson et al., 2019] and solved using the interior-point optimizer IPOPT [Wächter and Biegler, 2006] on an Intel i9-7940X CPU. |
| Experiment Setup | Yes | Table 1: Parameters and expressions for the CBF example Parameter Value f known(x, u) 0.5x + u 1 c(x, u) (f known(x, u) + f µ σ (x, u))2 + u2 umin 2 umax 2 γ 0.95 ω 104 |