This repository contains a PyTorch implementation of DLFM-VFRF, presented in the paper "Adaptive RKHS Fourier Features for Compositional Gaussian Process Models."

The implementation is mainly built on the GPyTorch package. requirements.txt contains a small list of package versions required to run the code.

The work proposes a set of RKHS Fourier features for GP models derived from a convolution operation governed by ODEs:

$$ \text{Cov}[f(t), v_m] = \int_{-\infty}^tG(t-\tau)\phi_m(\tau)\mathrm{d}\tau = \begin{cases} \frac{\cos(z_i(t-a)+\theta)}{\beta\sqrt{z_i^2+\gamma^2}} + \xi_i & i =0,\ldots,M,\\ \frac{\sin(z_i(t-a)+\theta)}{\beta\sqrt{z_i^2+\gamma^2}} + \xi_i & i =M+1,\ldots, 2M, \end{cases} $$ $$ \mathbf{\phi}(x) = [1, \cos(z_1(x-a)),\cdots,\cos(z_M(x-a)), \sin(z_1(x -a)),\cdots,\sin(z_M(x-a))], $$