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.

In many search applications related to passage retrieval, text entailment, and sub-graph search, the query and each'document' is a set of elements, with a document

Bayesian Optimization (BO) is a versatile method for global optimization of a black-box function using noisy point-wise observations.

Inthiswork,wefocuson imitation learning, where the aim is to learn how to act in the environment to match the behavior of some unknown targetpolicy [25].

Alternatively, the spectral kernels are defined in the spectral domain [2,13,14]. Nonetheless, when modeling graph-structured data, prior kernels face severalchallenges.