Regular Fourier Features for Nonstationary Gaussian Processes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915819889360896 |
|---|---|
| author | Jawaid, Arsalan Karatas, Abdullah Seewig, Jörg |
| author_facet | Jawaid, Arsalan Karatas, Abdullah Seewig, Jörg |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular Fourier Features for Nonstationary Gaussian Processes Jawaid, Arsalan Karatas, Abdullah Seewig, Jörg Machine Learning 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. |
| title | Regular Fourier Features for Nonstationary Gaussian Processes |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.23006 |