Regular Fourier Features for Nonstationary Gaussian Processes

• URL: http://arxiv.org/abs/2602.23006v1
• Date: Thu, 26 Feb 2026 13:50:28 GMT
• Title: Regular Fourier Features for Nonstationary Gaussian Processes
• Authors: Arsalan Jawaid, Abdullah Karatas, Jörg Seewig,
• Abstract summary: Spectral methods treat the spectral density as a probability distribution for Monte Carlo approximation.<n>We propose regular Fourier features for harmonizable processes that avoid this limitation.<n>We demonstrate the method on locally stationary kernels and on harmonizable mixture kernels with complex-valued spectral densities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation, treating the spectral density as a probability distribution for Monte Carlo approximation. Although this probabilistic interpretation works for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable processes that avoid this limitation. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Under a finite spectral support assumption, this yields an efficient low-rank approximation that is positive semi-definite by construction. When the spectral density is unknown, the framework extends naturally to kernel learning from data. We demonstrate the method on locally stationary kernels and on harmonizable mixture kernels with complex-valued spectral densities.

Related papers

• Avoiding spectral pollution for transfer operators using residuals [0.6116681488656472]
  We present algorithms for computing spectral properties of transfer operators without spectral pollution.<n>Case studies range from families of Blaschke maps with known spectrum to a molecular dynamics model of protein folding.<n>Our methods offer robust tools for spectral estimation across a broad range of applications.
  arXiv  Detail & Related papers  (2025-07-22T18:01:05Z)
• LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation [55.800319453296886]
  Time series with missing or irregularly sampled data are a persistent challenge in machine learning.<n>We introduce a different Lombiable--Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data.
  arXiv  Detail & Related papers  (2025-06-20T14:48:42Z)
• Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results [0.0]
  We identify the onset of quantum chaos and scrambling in quantum many-body systems.<n>We numerically show that Bethe Ansatz walkers fall into a category similar to the non-integrable walkers.
  arXiv  Detail & Related papers  (2025-05-08T12:56:06Z)
• A spectral mixture representation of isotropic kernels to generalize random Fourier features [0.0]
  Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution.<n>We show that the spectral distribution of positive definite isotropic kernels in $mathbbRd$ for all $dgeq1$ can be decomposed as a scale mixture of $alpha$-stable random vectors.
  arXiv  Detail & Related papers  (2024-11-05T03:28:01Z)
• Kernel Learning by quantum annealer [0.966840768820136]
  We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We show that it is possible to create a spectral distribution that could not be feasible with the Gaussian distribution.
  arXiv  Detail & Related papers  (2023-04-20T08:08:03Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• A Note on Optimizing Distributions using Kernel Mean Embeddings [94.96262888797257]
  Kernel mean embeddings represent probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. We show that when the kernel is characteristic, distributions with a kernel sum-of-squares density are dense. We provide algorithms to optimize such distributions in the finite-sample setting.
  arXiv  Detail & Related papers  (2021-06-18T08:33:45Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain [3.6526103325150383]
  We present a family of kernel that can approximate any stationary multi-output kernel to arbitrary precision. The proposed family of kernel represents the first multi-output generalisation of the spectral mixture kernel.
  arXiv  Detail & Related papers  (2021-03-11T20:54:51Z)
• Spectral density estimation with the Gaussian Integral Transform [91.3755431537592]
  spectral density operator $hatrho(omega)=delta(omega-hatH)$ plays a central role in linear response theory. We describe a near optimal quantum algorithm providing an approximation to the spectral density.
  arXiv  Detail & Related papers  (2020-04-10T03:14:38Z)
• Efficiently Sampling Functions from Gaussian Process Posteriors [76.94808614373609]
  We propose an easy-to-use and general-purpose approach for fast posterior sampling. We demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.
  arXiv  Detail & Related papers  (2020-02-21T14:03:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.