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 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.

翻译：深度高斯过程（DGPs）利用组合结构来建模非平稳过程。DGPs通常依赖于中间GP层的局部诱导点近似。DGP推断的最新进展表明，引入来自再生核希尔伯特空间（RKHS）的全局傅里叶特征可以增强DGPs捕捉复杂非平稳模式的能力。本文将此类特征的应用扩展到涉及线性变换的组合高斯过程。具体而言，我们引入了基于常微分方程（ODE）的RKHS傅里叶特征，该特征允许通过卷积操作实现自适应的振幅与相位调制。这一卷积形式将我们的工作与近期提出的深度潜在力模型联系起来，后者是一种专为建模非线性动力系统设计的多层结构。通过将这些可调节的RKHS傅里叶特征嵌入到双重随机变分推断框架中，我们的模型在多种回归任务上展现出更优的预测性能。