Adaptive RKHS Fourier Features for Compositional Gaussian Process Models
This work provides an incremental improvement for researchers in machine learning and statistics working with compositional Gaussian process models for complex regression problems.
The paper tackles the challenge of modeling non-stationary processes in Deep Gaussian Processes (DGPs) by introducing adaptive RKHS Fourier features with ODE-based amplitude and phase modulation, resulting in improved predictive performance across various regression tasks.
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.