# Frequency Domain Gaussian Process Models for H^∞ Uncertainties

arXiv: https://arxiv.org/abs/2211.15923 · HTML: https://mlsanity.com/paper/2211.15923/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Finite Sample Frequency Domain Identification](https://mlsanity.com/paper/2404.01100/) (2024)
- [Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis](https://mlsanity.com/paper/2508.17142/) (2025)

## Abstract (arXiv)

Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an H_∞ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers.