Adaptive RKHS Fourier Features for Compositional Gaussian Process Models

Abstract: Deep Gaussian Processes (DGPs) leverage a compositional structure to model non-stationary processes. DGPs typically rely on local inducing point approximations across intermediate GP layers. Recent advances in DGP inference have shown that incorporating global Fourier features from the Reproducing Kernel Hilbert Space (RKHS) can enhance the DGPs' capability to capture complex non-stationary patterns. This paper extends the use of these features to compositional GPs involving linear transformations. In particular, we introduce Ordinary Differential Equation(ODE)--based RKHS Fourier features that allow for adaptive amplitude and phase modulation through convolution operations. This convolutional formulation relates our work to recently proposed deep latent force models, a multi-layer structure designed for modelling nonlinear dynamical systems. By embedding these adjustable RKHS Fourier features within a doubly stochastic variational inference framework, our model exhibits improved predictive performance across various regression tasks.