Scalable Gaussian Process Regression via Deterministic Trigonometric Features: Uniform Bounds for Safe Model Predictive Control

What the math gives to ML

The paper offers a constructive way to replace a data-scaled Gaussian process with Bayesian linear regression over deterministic trigonometric features while retaining a high-probability uncertainty bound that is uniform over the entire bounded input domain. The transferable asset is the combination of finite-dimensional sufficient statistics, closed-form posterior variance, and a domain-wide confidence envelope suitable for safety decisions. A strong neural-network transfer is to use a deterministic Fourier feature map with a Bayesian linear output head, then use its uniform uncertainty envelope to gate updates, exploration, or deployment. The certificate is falsifiable: posterior computation should become independent of dataset size after feature sufficient statistics are accumulated, and empirical residuals should remain below the predicted envelope simultaneously over a held-out domain at the claimed confidence level.